%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, unsorted: $tType).
thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
thf(type_def_7, type, d_unsorted: $tType).
thf(func_def_0, type, subrel: (($i > $i > $o) > ($i > $i > $o) > $o)).
thf(func_def_1, type, inv: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_2, type, idem: ((($i > $i > $o) > $i > $i > $o) > $o)).
thf(func_def_3, type, infl: ((($i > $i > $o) > $i > $i > $o) > $o)).
thf(func_def_4, type, mono: ((($i > $i > $o) > $i > $i > $o) > $o)).
thf(func_def_5, type, refl: (($i > $i > $o) > $o)).
thf(func_def_6, type, irrefl: (($i > $i > $o) > $o)).
thf(func_def_7, type, rc: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_8, type, symm: (($i > $i > $o) > $o)).
thf(func_def_9, type, antisymm: (($i > $i > $o) > $o)).
thf(func_def_10, type, asymm: (($i > $i > $o) > $o)).
thf(func_def_11, type, sc: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_12, type, trans: (($i > $i > $o) > $o)).
thf(func_def_13, type, tc: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_14, type, trc: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_15, type, trsc: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_16, type, po: (($i > $i > $o) > $o)).
thf(func_def_17, type, so: (($i > $i > $o) > $o)).
thf(func_def_18, type, total: (($i > $i > $o) > $o)).
thf(func_def_19, type, term: (($i > $i > $o) > $o)).
thf(func_def_20, type, ind: (($i > $i > $o) > $o)).
thf(func_def_21, type, innf: (($i > $i > $o) > $i > $o)).
thf(func_def_22, type, nfof: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_23, type, norm: (($i > $i > $o) > $o)).
thf(func_def_24, type, join: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_25, type, lconfl: (($i > $i > $o) > $o)).
thf(func_def_26, type, sconfl: (($i > $i > $o) > $o)).
thf(func_def_27, type, confl: (($i > $i > $o) > $o)).
thf(func_def_28, type, cr: (($i > $i > $o) > $o)).
thf(func_def_29, type, d2unsorted: (d_unsorted > $i)).
thf(func_def_30, type, d_unsorted_0: d_unsorted).
thf(func_def_32, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_33, type, vOR: ($o > $o > $o)).
thf(func_def_34, type, db3: !>[X0: $tType]:(X0)).
thf(func_def_35, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_36, type, db4: !>[X0: $tType]:(X0)).
thf(func_def_37, type, vAND: ($o > $o > $o)).
thf(func_def_38, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_39, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_40, type, vNOT: ($o > $o)).
thf(func_def_41, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_42, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_43, type, db8: !>[X0: $tType]:(X0)).
thf(func_def_44, type, db5: !>[X0: $tType]:(X0)).
thf(func_def_45, type, db9: !>[X0: $tType]:(X0)).
thf(func_def_46, type, db6: !>[X0: $tType]:(X0)).
thf(func_def_47, type, db7: !>[X0: $tType]:(X0)).
thf(func_def_48, type, vIMP: ($o > $o > $o)).
thf(func_def_49, type, sK0: ($i > d_unsorted)).
thf(func_def_53, type, sK2: ($i > $i > $o)).
thf(func_def_57, type, sK6: ($i > ($i > $i > $o) > $i > $i > $i > $o)).
thf(func_def_58, type, sK7: ($i > ($i > $i > $o) > $i > $i > $i > $o)).
thf(func_def_59, type, sK8: ($i > ($i > $i > $o) > $i > $i > $i > $o)).
thf(func_def_60, type, sK9: ($i > ($i > $i > $o) > $i > $i > $i > $o)).
thf(func_def_61, type, sK10: ($i > ($i > $i > $o) > $i > $i)).
thf(func_def_62, type, sK11: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_63, type, sK12: (($i > $i > $o) > $i)).
thf(func_def_64, type, sK13: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_65, type, sK14: (($i > $i > $o) > $i)).
thf(func_def_66, type, sK15: (($i > $i > $o) > $i)).
thf(func_def_67, type, sK16: (($i > $i > $o) > $i)).
thf(func_def_68, type, sK17: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_69, type, sK18: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_70, type, sK19: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_71, type, sK20: (($i > $i > $o) > $i)).
thf(func_def_72, type, sK21: (($i > $i > $o) > $i)).
thf(func_def_73, type, sK22: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_74, type, sK23: (($i > $i > $o) > $i)).
thf(func_def_75, type, sK24: (($i > $i > $o) > $i)).
thf(func_def_76, type, sK25: (($i > $i > $o) > $i)).
thf(func_def_77, type, sK26: (($i > $i > $o) > $i)).
thf(func_def_78, type, sK27: (($i > $i > $o) > $i)).
thf(func_def_79, type, sK28: (($i > $i > $o) > $i)).
thf(func_def_80, type, sK29: (($i > $i > $o) > $i)).
thf(func_def_81, type, sK30: (($i > $i > $o) > $i)).
thf(func_def_82, type, sK31: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_83, type, sK32: (($i > $i > $o) > $i)).
thf(func_def_84, type, sK33: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_85, type, sK34: (($i > $i > $o) > $i)).
thf(func_def_86, type, sK35: (($i > $i > $o) > $i)).
thf(func_def_87, type, sK36: (($i > $i > $o) > $i)).
thf(func_def_88, type, sK37: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_89, type, sK38: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_90, type, sK39: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_91, type, sK40: (($i > $i > $o) > $i)).
thf(func_def_92, type, sK41: (($i > $i > $o) > $i)).
thf(func_def_93, type, sK42: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_94, type, sK43: (($i > $i > $o) > $i)).
thf(func_def_95, type, sK44: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_96, type, sK45: (($i > $i > $o) > $i)).
thf(func_def_97, type, sK46: (($i > $i > $o) > $i)).
thf(func_def_98, type, sK47: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_99, type, sK48: (($i > $i > $o) > $i)).
thf(func_def_100, type, sK49: (($i > $i > $o) > $i)).
thf(func_def_101, type, sK50: (($i > $i > $o) > $i)).
thf(func_def_102, type, sK51: (($i > $i > $o) > $i)).
thf(func_def_103, type, sK52: (($i > $i > $o) > $i)).
thf(func_def_104, type, sK53: (($i > $i > $o) > $i)).
thf(func_def_105, type, sK54: (($i > $i > $o) > $i)).
thf(func_def_106, type, sK55: (($i > $i > $o) > $i)).
thf(func_def_107, type, sK56: (($i > $i > $o) > $i)).
thf(func_def_108, type, sK57: (($i > $i > $o) > $i)).
thf(func_def_109, type, sK58: (($i > $i > $o) > $i)).
thf(func_def_110, type, sK59: (($i > $i > $o) > $i)).
thf(func_def_111, type, sK60: (($i > $i > $o) > $i)).
thf(func_def_112, type, sK61: (($i > $i > $o) > $i)).
thf(func_def_113, type, sK62: (($i > $i > $o) > $i)).
thf(func_def_114, type, sK63: (($i > $i > $o) > $i)).
thf(func_def_115, type, sK64: (($i > $i > $o) > $i)).
thf(func_def_116, type, sK65: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_117, type, sK66: (($i > $i > $o) > $i)).
thf(func_def_118, type, sK67: (($i > $i > $o) > $i)).
thf(func_def_119, type, sK68: (($i > $i > $o) > $i)).
thf(func_def_120, type, sK69: (($i > $i > $o) > $i)).
thf(func_def_121, type, sK70: (($i > $i > $o) > $i)).
thf(func_def_122, type, sK71: (($i > $i > $o) > $i)).
thf(func_def_123, type, sK72: (($i > $i > $o) > $i)).
thf(func_def_124, type, sK73: (($i > $i > $o) > $i)).
thf(func_def_125, type, sK74: (($i > $i > $o) > $i)).
thf(func_def_126, type, sK75: ($i > ($i > $i > $o) > $i > $i)).
thf(func_def_127, type, sK76: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_128, type, sK77: (($i > $i > $o) > $i)).
thf(func_def_129, type, sK78: (($i > $i > $o) > $i)).
thf(func_def_130, type, sK79: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_131, type, sK80: (($i > $i > $o) > $i)).
thf(func_def_132, type, sK81: (($i > $i > $o) > $i)).
thf(func_def_133, type, sK82: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_134, type, sK83: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_135, type, sK84: (($i > $i > $o) > $i)).
thf(func_def_136, type, sK85: (($i > $i > $o) > $i)).
thf(func_def_137, type, sK86: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_138, type, sK87: (($i > $i > $o) > $i)).
thf(func_def_139, type, sK88: (($i > $i > $o) > $i)).
thf(func_def_140, type, sK89: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_141, type, sK90: (($i > $i > $o) > $i)).
thf(func_def_142, type, sK91: (($i > $i > $o) > $i)).
thf(func_def_143, type, sK92: (($i > $i > $o) > $i)).
thf(func_def_144, type, sK93: (($i > $i > $o) > $i)).
thf(func_def_145, type, sK94: (($i > $i > $o) > $i)).
thf(func_def_146, type, sK95: (($i > $i > $o) > $i)).
thf(func_def_147, type, sK96: (($i > $i > $o) > $i)).
thf(func_def_148, type, sK97: (($i > $i > $o) > $i)).
thf(func_def_149, type, sK98: (($i > $i > $o) > $i)).
thf(func_def_150, type, sK99: (($i > $i > $o) > $i)).
thf(func_def_151, type, sK100: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_152, type, sK101: (($i > $i > $o) > $i)).
thf(func_def_153, type, sK102: (($i > $i > $o) > $i)).
thf(func_def_154, type, sK103: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_155, type, sK104: (($i > $i > $o) > $i)).
thf(func_def_156, type, sK105: (($i > $i > $o) > $i)).
thf(func_def_157, type, sK106: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_158, type, sK107: (($i > $i > $o) > $i)).
thf(func_def_159, type, sK108: (($i > $i > $o) > $i)).
thf(func_def_160, type, sK109: (($i > $i > $o) > $i)).
thf(func_def_161, type, sK110: (($i > $i > $o) > $i)).
thf(func_def_162, type, sK111: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_163, type, sK112: (($i > $i > $o) > $i)).
thf(func_def_164, type, sK113: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_165, type, sK114: (($i > $i > $o) > $i)).
thf(func_def_166, type, sK115: (($i > $i > $o) > $i)).
thf(func_def_167, type, sK116: (($i > $i > $o) > $i)).
thf(func_def_168, type, sK117: (($i > $i > $o) > $i)).
thf(func_def_169, type, sK118: (($i > $i > $o) > $i)).
thf(func_def_170, type, sK119: (($i > $i > $o) > $i)).
thf(func_def_171, type, sK120: (($i > $i > $o) > $i)).
thf(func_def_172, type, sK121: (($i > $i > $o) > $i)).
thf(func_def_173, type, sK122: (($i > $i > $o) > $i)).
thf(func_def_174, type, sK123: (($i > $i > $o) > $i)).
thf(func_def_175, type, sK124: (($i > $i > $o) > $i)).
thf(func_def_176, type, sK125: (($i > $i > $o) > $i)).
thf(func_def_177, type, sK126: (($i > $i > $o) > $i)).
thf(func_def_178, type, sK127: (($i > $i > $o) > $i)).
thf(func_def_179, type, sK128: (($i > $i > $o) > $i)).
thf(func_def_180, type, sK129: (($i > $i > $o) > $i)).
thf(func_def_181, type, sK130: (($i > $i > $o) > $i)).
thf(func_def_182, type, sK131: (($i > $i > $o) > $i)).
thf(func_def_183, type, sK132: (($i > $i > $o) > $i)).
thf(func_def_184, type, sK133: (($i > $i > $o) > $i)).
thf(func_def_185, type, sK134: (($i > $i > $o) > $i)).
thf(func_def_186, type, sK135: (($i > $i > $o) > $i)).
thf(func_def_187, type, sK136: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_188, type, sK137: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_189, type, sK138: (($i > $i > $o) > $i)).
thf(func_def_190, type, sK139: (($i > $i > $o) > $i)).
thf(func_def_191, type, sK140: (($i > $i > $o) > $i)).
thf(func_def_192, type, sK141: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_193, type, sK142: (($i > $i > $o) > $i)).
thf(func_def_194, type, sK143: (($i > $i > $o) > $i)).
thf(func_def_195, type, sK144: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_196, type, sK145: (($i > $i > $o) > $i)).
thf(func_def_197, type, sK146: (($i > $i > $o) > $i)).
thf(func_def_198, type, sK147: (($i > $i > $o) > $i)).
thf(func_def_199, type, sK148: (($i > $i > $o) > $i)).
thf(func_def_200, type, sK149: (($i > $i > $o) > $i)).
thf(func_def_201, type, sK150: (($i > $i > $o) > $i)).
thf(func_def_202, type, sK151: (($i > $i > $o) > $i)).
thf(func_def_203, type, sK152: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_204, type, sK153: (($i > $i > $o) > $i)).
thf(func_def_205, type, sK154: (($i > $i > $o) > $i)).
thf(func_def_206, type, sK155: (($i > $i > $o) > $i)).
thf(func_def_207, type, sK156: (($i > $i > $o) > $i)).
thf(func_def_208, type, sK157: (($i > $i > $o) > $i)).
thf(func_def_209, type, sK158: (($i > $i > $o) > $i)).
thf(func_def_210, type, sK159: (($i > $i > $o) > $i)).
thf(func_def_211, type, sK160: (($i > $i > $o) > $i)).
thf(func_def_212, type, sK161: (($i > $i > $o) > $i)).
thf(func_def_213, type, sK162: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_214, type, sK163: (($i > $i > $o) > $i)).
thf(func_def_215, type, sK164: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_216, type, sK165: (($i > $i > $o) > $i)).
thf(func_def_217, type, sK166: (($i > $i > $o) > $i)).
thf(func_def_218, type, sK167: (($i > $i > $o) > $i)).
thf(func_def_219, type, sK168: (($i > $i > $o) > $i)).
thf(func_def_220, type, sK169: (($i > $i > $o) > $i)).
thf(func_def_221, type, sK170: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_222, type, sK171: (($i > $i > $o) > $i)).
thf(func_def_223, type, sK172: (($i > $i > $o) > $i)).
thf(func_def_224, type, sK173: (($i > $i > $o) > $i)).
thf(func_def_225, type, sK174: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_226, type, sK175: (($i > $i > $o) > $i)).
thf(func_def_227, type, sK176: (($i > $i > $o) > $i)).
thf(func_def_228, type, sK177: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_229, type, sK178: (($i > $i > $o) > $i)).
thf(func_def_230, type, sK179: (($i > $i > $o) > $i)).
thf(func_def_231, type, sK180: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_232, type, sK181: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_233, type, sK182: (($i > $i > $o) > $i)).
thf(func_def_234, type, sK183: (($i > $i > $o) > $i)).
thf(func_def_235, type, sK184: (($i > $i > $o) > $i)).
thf(func_def_236, type, sK185: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_237, type, sK186: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_238, type, sK187: (($i > $i > $o) > $i)).
thf(func_def_239, type, sK188: (($i > $i > $o) > $i)).
thf(func_def_240, type, sK189: (($i > $i > $o) > $i)).
thf(func_def_241, type, sK190: (($i > $i > $o) > $i)).
thf(func_def_242, type, sK191: (($i > $i > $o) > $i)).
thf(func_def_243, type, sK192: (($i > $i > $o) > $i)).
thf(func_def_244, type, sK193: (($i > $i > $o) > $i)).
thf(func_def_245, type, sK194: (($i > $i > $o) > $i)).
thf(func_def_246, type, sK195: (($i > $i > $o) > $i)).
thf(func_def_247, type, sK196: (($i > $i > $o) > $i)).
thf(func_def_248, type, sK197: (($i > $i > $o) > $i)).
thf(func_def_249, type, sK198: (($i > $i > $o) > $i)).
thf(func_def_250, type, sK199: (($i > $i > $o) > $i)).
thf(func_def_251, type, sK200: (($i > $i > $o) > $i)).
thf(func_def_252, type, sK201: (($i > $i > $o) > $i)).
thf(func_def_253, type, sK202: (($i > $i > $o) > $i)).
thf(func_def_254, type, sK203: (($i > $i > $o) > $i)).
thf(func_def_255, type, sK204: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_256, type, sK205: (($i > $i > $o) > $i)).
thf(func_def_257, type, sK206: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_258, type, sK207: (($i > $i > $o) > $i)).
thf(func_def_259, type, sK208: (($i > $i > $o) > $i)).
thf(func_def_260, type, sK209: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_261, type, sK210: (($i > $i > $o) > $i)).
thf(func_def_262, type, sK211: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_263, type, sK212: (($i > $i > $o) > $i)).
thf(func_def_264, type, sK213: (($i > $i > $o) > $i)).
thf(func_def_265, type, sK214: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_266, type, sK215: (($i > $i > $o) > $i)).
thf(func_def_267, type, sK216: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_268, type, sK217: (($i > $i > $o) > $i)).
thf(func_def_269, type, sK218: (($i > $i > $o) > $i)).
thf(func_def_270, type, sK219: (($i > $i > $o) > $i)).
thf(func_def_271, type, sK220: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_272, type, sK221: (($i > $i > $o) > $i)).
thf(func_def_273, type, sK222: (($i > $i > $o) > $i)).
thf(func_def_274, type, sK223: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_275, type, sK224: (($i > $i > $o) > $i)).
thf(func_def_276, type, sK225: (($i > $i > $o) > $i)).
thf(func_def_277, type, sK226: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_278, type, sK227: (($i > $i > $o) > $i)).
thf(func_def_279, type, sK228: (($i > $i > $o) > $i)).
thf(func_def_280, type, sK229: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_281, type, sK230: (($i > $i > $o) > $i)).
thf(func_def_282, type, sK231: (($i > $i > $o) > $i)).
thf(func_def_283, type, sK232: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_284, type, sK233: (($i > $i > $o) > $i)).
thf(func_def_285, type, sK234: (($i > $i > $o) > $i)).
thf(func_def_286, type, sK235: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_287, type, sK236: (($i > $i > $o) > $i)).
thf(func_def_288, type, sK237: (($i > $i > $o) > $i)).
thf(func_def_289, type, sK238: (($i > $i > $o) > $i)).
thf(func_def_290, type, sK239: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_291, type, sK240: (($i > $i > $o) > $i)).
thf(func_def_292, type, sK241: (($i > $i > $o) > $i)).
thf(func_def_293, type, sK242: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_294, type, sK243: (($i > $i > $o) > $i)).
thf(func_def_295, type, sK244: (($i > $i > $o) > $i)).
thf(func_def_296, type, sK245: (($i > $i > $o) > $i)).
thf(func_def_297, type, sK246: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_298, type, sK247: (($i > $i > $o) > $i)).
thf(func_def_299, type, sK248: (($i > $i > $o) > $i)).
thf(func_def_300, type, sK249: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_301, type, sK250: (($i > $i > $o) > $i)).
thf(func_def_302, type, sK251: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_303, type, sK252: (($i > $i > $o) > $i)).
thf(func_def_304, type, sK253: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_305, type, sK254: (($i > $i > $o) > $i)).
thf(func_def_306, type, sK255: (($i > $i > $o) > $i)).
thf(func_def_307, type, sK256: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_308, type, sK257: (($i > $i > $o) > $i)).
thf(func_def_309, type, sK258: (($i > $i > $o) > ($i > $i > $o) > $i)).
thf(func_def_310, type, sK259: (($i > $i > $o) > $i)).
thf(func_def_311, type, sK260: (($i > $i > $o) > $i)).
thf(func_def_312, type, sK261: (($i > $i > $o) > $i)).
thf(func_def_313, type, sK262: (($i > $i > $o) > $i)).
thf(func_def_314, type, sK263: (($i > $i > $o) > $i)).
thf(func_def_315, type, sK264: (($i > $i > $o) > $i)).
thf(func_def_316, type, sK265: (($i > $i > $o) > $i)).
thf(func_def_317, type, sK266: (($i > $i > $o) > $i)).
thf(func_def_318, type, sK267: (($i > $i > $o) > $i)).
thf(func_def_319, type, sK268: (($i > $i > $o) > $i)).
thf(func_def_320, type, sK269: (($i > $i > $o) > $i)).
thf(func_def_321, type, sK270: (($i > $i > $o) > $i)).
thf(func_def_322, type, sK271: (($i > $i > $o) > $i)).
thf(func_def_323, type, sK272: (($i > $i > $o) > $i)).
thf(func_def_324, type, sK273: (($i > $i > $o) > $i)).
thf(func_def_325, type, sK274: (($i > $i > $o) > $i)).
thf(func_def_326, type, sK275: (($i > $i > $o) > $i)).
thf(func_def_327, type, sK276: (($i > $i > $o) > $i)).
thf(func_def_328, type, sK277: (($i > $i > $o) > $i)).
thf(func_def_329, type, sK278: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_330, type, sK279: (($i > $i > $o) > $i)).
thf(func_def_331, type, sK280: (($i > $i > $o) > $i > $i > $o)).
thf(func_def_332, type, sK281: (($i > $i > $o) > $i)).
thf(func_def_333, type, sK282: (($i > $i > $o) > $i)).
thf(func_def_334, type, sK283: (($i > $i > $o) > $i > $i > $i > $o)).
thf(func_def_335, type, sK284: (($i > $i > $o) > $i > $i > $i > $o)).
thf(f1,axiom,(
  ((^[X2 : ($i > $i > $o), X4 : $i, X5 : $i] : ((X2 @ X5 @ X4))) = inv) & (irrefl = (^[X2 : ($i > $i > $o)] : (! [X4 : $i] : ~(X2 @ X4 @ X4)))) & (norm = (^[X2 : ($i > $i > $o)] : (! [X30 : $i,X4 : $i] : (~ ! [X31 : $i] : (~ ! [X16 : $i] : ~(X2 @ X31 @ X16) | ~ ! [X3 : ($i > $i > $o)] : ((X3 @ X4 @ X31) | ~ ! [X8 : $i,X9 : $i] : ((X3 @ X8 @ X9) | ~(X2 @ X8 @ X9)) | ~ ! [X11 : $i,X7 : $i,X10 : $i] : (~(X3 @ X11 @ X7) | (X3 @ X10 @ X7) | ~(X3 @ X10 @ X11)))) | ~(X2 @ X4 @ X30))))) & ! [X37 : $i] : ? [X36 : d_unsorted] : (X37 = ((d2unsorted @ X36))) & ((^[X2 : ($i > $i > $o), X12 : $i, X13 : $i] : ((X12 = X13) | ! [X3 : ($i > $i > $o)] : (~ ! [X11 : $i,X7 : $i,X10 : $i] : (~(X3 @ X11 @ X7) | (X3 @ X10 @ X7) | ~(X3 @ X10 @ X11)) | ~ ! [X9 : $i,X8 : $i] : (~(X2 @ X8 @ X9) | (X3 @ X8 @ X9)) | (X3 @ X12 @ X13)))) = trc) & ((^[X2 : ($i > $i > $o), X4 : $i, X5 : $i] : (! [X3 : ($i > $i > $o)] : (~ ! [X11 : $i,X7 : $i,X10 : $i] : (~(X3 @ X11 @ X7) | ~(X3 @ X10 @ X11) | (X3 @ X10 @ X7)) | (X3 @ X4 @ X5) | ~ ! [X9 : $i,X8 : $i] : ((X3 @ X8 @ X9) | ~(X2 @ X8 @ X9))))) = tc) & ((^[X2 : ($i > $i > $o), X4 : $i] : (! [X5 : $i] : ~(X2 @ X4 @ X5))) = innf) & ! [X36 : d_unsorted] : (X36 = d_unsorted_0) & ((^[X2 : ($i > $i > $o)] : (! [X4 : $i,X7 : $i,X5 : $i] : (~(X2 @ X4 @ X5) | (X2 @ X4 @ X7) | ~(X2 @ X5 @ X7)) & ! [X4 : $i,X5 : $i] : (~(X2 @ X4 @ X5) | ~(X2 @ X5 @ X4) | (X4 = X5)) & ! [X4 : $i] : (X2 @ X4 @ X4))) = po) & (join = (^[X2 : ($i > $i > $o), X4 : $i, X5 : $i] : (~(! [X21 : $i] : (~ ! [X3 : ($i > $i > $o)] : (~ ! [X9 : $i,X8 : $i] : ((X3 @ X8 @ X9) | ~(X2 @ X8 @ X9)) | ~ ! [X11 : $i,X20 : $i,X10 : $i] : ((X3 @ X10 @ X20) | ~(X3 @ X11 @ X20) | ~(X3 @ X10 @ X11)) | (X3 @ X5 @ X21)) | ~ ! [X3 : ($i > $i > $o)] : (~ ! [X8 : $i,X9 : $i] : (~(X2 @ X8 @ X9) | (X3 @ X8 @ X9)) | ~ ! [X11 : $i,X10 : $i,X19 : $i] : (~(X3 @ X11 @ X19) | (X3 @ X10 @ X19) | ~(X3 @ X10 @ X11)) | (X3 @ X4 @ X21))) & ~ ! [X3 : ($i > $i > $o)] : ((X3 @ X5 @ X4) | ~ ! [X9 : $i,X8 : $i] : (~(X2 @ X8 @ X9) | (X3 @ X8 @ X9)) | ~ ! [X11 : $i,X20 : $i,X10 : $i] : ((X3 @ X10 @ X20) | ~(X3 @ X11 @ X20) | ~(X3 @ X10 @ X11))) & (X4 != X5) & ~ ! [X3 : ($i > $i > $o)] : ((X3 @ X4 @ X5) | ~ ! [X11 : $i,X10 : $i,X19 : $i] : ((X3 @ X10 @ X19) | ~(X3 @ X10 @ X11) | ~(X3 @ X11 @ X19)) | ~ ! [X8 : $i,X9 : $i] : ((X3 @ X8 @ X9) | ~(X2 @ X8 @ X9))))))) & (nfof = (^[X2 : ($i > $i > $o), X4 : $i, X5 : $i] : ((! [X3 : ($i > $i > $o)] : (~ ! [X8 : $i,X9 : $i] : ((X3 @ X8 @ X9) | ~(X2 @ X8 @ X9)) | ~ ! [X7 : $i,X11 : $i,X10 : $i] : ((X3 @ X10 @ X7) | ~(X3 @ X10 @ X11) | ~(X3 @ X11 @ X7)) | (X3 @ X5 @ X4)) | (X4 = X5)) & ! [X16 : $i] : ~(X2 @ X4 @ X16)))) & ((^[X2 : ($i > $i > $o)] : (! [X5 : $i,X4 : $i,X29 : ($i > $i > $o),X7 : $i,X28 : ($i > $i > $o)] : (~ ! [X21 : $i] : (~ ! [X3 : ($i > $i > $o)] : ((X3 @ X7 @ X21) | ~ ! [X9 : $i,X8 : $i] : (~(X2 @ X8 @ X9) | (X3 @ X8 @ X9)) | ~ ! [X10 : $i,X11 : $i,X19 : $i] : (~(X3 @ X10 @ X11) | (X3 @ X10 @ X19) | ~(X3 @ X11 @ X19))) | ~ ! [X3 : ($i > $i > $o)] : ((X3 @ X5 @ X21) | ~ ! [X9 : $i,X8 : $i] : ((X3 @ X8 @ X9) | ~(X2 @ X8 @ X9)) | ~ ! [X11 : $i,X20 : $i,X10 : $i] : (~(X3 @ X10 @ X11) | ~(X3 @ X11 @ X20) | (X3 @ X10 @ X20)))) | (X29 @ X7 @ X5) | (X28 @ X5 @ X7) | ~ ! [X10 : $i,X11 : $i,X19 : $i] : (~(X29 @ X11 @ X19) | ~(X29 @ X10 @ X11) | (X29 @ X10 @ X19)) | ~ ! [X8 : $i,X9 : $i] : (~(X2 @ X8 @ X9) | (X29 @ X8 @ X9)) | (X5 = X7) | ~(X2 @ X4 @ X5) | ~ ! [X8 : $i,X9 : $i] : ((X28 @ X8 @ X9) | ~(X2 @ X8 @ X9)) | ~ ! [X20 : $i,X10 : $i,X11 : $i] : (~(X28 @ X11 @ X20) | (X28 @ X10 @ X20) | ~(X28 @ X10 @ X11)) | ~(X2 @ X4 @ X7)))) = lconfl) & (sconfl = (^[X2 : ($i > $i > $o)] : (! [X4 : $i,X25 : ($i > $i > $o),X5 : $i,X26 : ($i > $i > $o),X7 : $i] : (~ ! [X19 : $i,X10 : $i,X11 : $i] : (~(X26 @ X11 @ X19) | (X26 @ X10 @ X19) | ~(X26 @ X10 @ X11)) | ~ ! [X21 : $i] : (~ ! [X3 : ($i > $i > $o)] : (~ ! [X19 : $i,X11 : $i,X10 : $i] : (~(X3 @ X10 @ X11) | ~(X3 @ X11 @ X19) | (X3 @ X10 @ X19)) | (X3 @ X7 @ X21) | ~ ! [X9 : $i,X8 : $i] : ((X3 @ X8 @ X9) | ~(X2 @ X8 @ X9))) | ~ ! [X3 : ($i > $i > $o)] : (~ ! [X8 : $i,X9 : $i] : ((X3 @ X8 @ X9) | ~(X2 @ X8 @ X9)) | ~ ! [X20 : $i,X11 : $i,X10 : $i] : ((X3 @ X10 @ X20) | ~(X3 @ X11 @ X20) | ~(X3 @ X10 @ X11)) | (X3 @ X5 @ X21))) | ~(X2 @ X4 @ X7) | (~ ! [X3 : ($i > $i > $o)] : (~ ! [X8 : $i,X9 : $i] : ((X3 @ X8 @ X9) | ~(X2 @ X8 @ X9)) | ~ ! [X10 : $i,X27 : $i,X11 : $i] : (~(X3 @ X11 @ X27) | (X3 @ X10 @ X27) | ~(X3 @ X10 @ X11)) | (X3 @ X4 @ X5)) & (X4 != X5)) | (X26 @ X7 @ X5) | ~ ! [X9 : $i,X8 : $i] : (~(X2 @ X8 @ X9) | (X26 @ X8 @ X9)) | (X5 = X7) | ~ ! [X10 : $i,X11 : $i,X20 : $i] : ((X25 @ X10 @ X20) | ~(X25 @ X11 @ X20) | ~(X25 @ X10 @ X11)) | ~ ! [X9 : $i,X8 : $i] : ((X25 @ X8 @ X9) | ~(X2 @ X8 @ X9)) | (X25 @ X5 @ X7))))) & (ind = (^[X2 : ($i > $i > $o)] : (! [X33 : $i,X32 : ($i > $o)] : (~ ! [X4 : $i] : (~ ! [X5 : $i] : (~ ! [X3 : ($i > $i > $o)] : (~ ! [X9 : $i,X8 : $i] : (~(X2 @ X8 @ X9) | (X3 @ X8 @ X9)) | ~ ! [X10 : $i,X11 : $i,X7 : $i] : ((X3 @ X10 @ X7) | ~(X3 @ X10 @ X11) | ~(X3 @ X11 @ X7)) | (X3 @ X4 @ X5)) | (X32 @ X5)) | (X32 @ X4)) | (X32 @ X33))))) & (total = (^[X2 : ($i > $i > $o)] : (! [X4 : $i,X5 : $i] : ((X2 @ X5 @ X4) | (X4 = X5) | (X2 @ X4 @ X5))))) & ((^[X2 : ($i > $i > $o), X4 : $i, X5 : $i] : ((X2 @ X4 @ X5) | (X4 = X5))) = rc) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X0)) = ((d2unsorted @ X1))) => (X0 = X1)) & ((^[X6 : (($i > $i > $o) > $i > $i > $o)] : (! [X4 : $i,X2 : ($i > $i > $o),X5 : $i] : ((X6 @ X2 @ X4 @ X5) | ~(X2 @ X4 @ X5)))) = infl) & (antisymm = (^[X2 : ($i > $i > $o)] : (! [X5 : $i,X4 : $i] : (~(X2 @ X4 @ X5) | (X4 = X5) | ~(X2 @ X5 @ X4))))) & ((^[X2 : ($i > $i > $o), X4 : $i, X5 : $i] : ((X2 @ X5 @ X4) | (X2 @ X4 @ X5))) = sc) & (term = (^[X2 : ($i > $i > $o)] : (! [X15 : $i,X14 : ($i > $o)] : (~ ! [X4 : $i] : (~(X14 @ X4) | ~ ! [X5 : $i] : (~(X2 @ X4 @ X5) | ~(X14 @ X5))) | ~(X14 @ X15))))) & (mono = (^[X6 : (($i > $i > $o) > $i > $i > $o)] : (! [X34 : $i,X3 : ($i > $i > $o),X35 : $i,X2 : ($i > $i > $o)] : ((X6 @ X3 @ X34 @ X35) | ~(X6 @ X2 @ X34 @ X35) | ~ ! [X5 : $i,X4 : $i] : ((X3 @ X4 @ X5) | ~(X2 @ X4 @ X5)))))) & (refl = (^[X2 : ($i > $i > $o)] : (! [X4 : $i] : (X2 @ X4 @ X4)))) & (symm = (^[X2 : ($i > $i > $o)] : (! [X5 : $i,X4 : $i] : (~(X2 @ X4 @ X5) | (X2 @ X5 @ X4))))) & ((^[X2 : ($i > $i > $o), X3 : ($i > $i > $o)] : (! [X5 : $i,X4 : $i] : (~(X2 @ X4 @ X5) | (X3 @ X4 @ X5)))) = subrel) & ((^[X2 : ($i > $i > $o), X12 : $i, X13 : $i] : (! [X3 : ($i > $i > $o)] : ((X3 @ X13 @ X12) | ~ ! [X9 : $i,X8 : $i] : (~(X2 @ X8 @ X9) | (X3 @ X8 @ X9)) | ~ ! [X11 : $i,X7 : $i,X10 : $i] : (~(X3 @ X10 @ X11) | (X3 @ X10 @ X7) | ~(X3 @ X11 @ X7))) | ! [X3 : ($i > $i > $o)] : (~ ! [X7 : $i,X10 : $i,X11 : $i] : (~(X3 @ X10 @ X11) | (X3 @ X10 @ X7) | ~(X3 @ X11 @ X7)) | ~ ! [X8 : $i,X9 : $i] : (~(X2 @ X8 @ X9) | (X3 @ X8 @ X9)) | (X3 @ X12 @ X13)) | (X12 = X13))) = trsc) & ((^[X2 : ($i > $i > $o)] : (! [X24 : ($i > $i > $o),X23 : ($i > $i > $o),X4 : $i,X5 : $i] : ((X24 @ X4 @ X5) | ~ ! [X8 : $i,X9 : $i] : (~(X2 @ X8 @ X9) | (X24 @ X8 @ X9)) | ((X4 != X5) & ~ ! [X3 : ($i > $i > $o)] : ((X3 @ X4 @ X5) | ~ ! [X11 : $i,X7 : $i,X10 : $i] : ((X3 @ X10 @ X7) | ~(X3 @ X11 @ X7) | ~(X3 @ X10 @ X11)) | ~ ! [X9 : $i,X8 : $i] : (~(X2 @ X8 @ X9) | (X3 @ X8 @ X9))) & ~ ! [X3 : ($i > $i > $o)] : (~ ! [X10 : $i,X11 : $i,X7 : $i] : ((X3 @ X10 @ X7) | ~(X3 @ X11 @ X7) | ~(X3 @ X10 @ X11)) | (X3 @ X5 @ X4) | ~ ! [X8 : $i,X9 : $i] : (~(X2 @ X8 @ X9) | (X3 @ X8 @ X9)))) | ~ ! [X21 : $i] : (~ ! [X3 : ($i > $i > $o)] : ((X3 @ X5 @ X21) | ~ ! [X10 : $i,X20 : $i,X11 : $i] : ((X3 @ X10 @ X20) | ~(X3 @ X11 @ X20) | ~(X3 @ X10 @ X11)) | ~ ! [X8 : $i,X9 : $i] : (~(X2 @ X8 @ X9) | (X3 @ X8 @ X9))) | ~ ! [X3 : ($i > $i > $o)] : ((X3 @ X4 @ X21) | ~ ! [X9 : $i,X8 : $i] : ((X3 @ X8 @ X9) | ~(X2 @ X8 @ X9)) | ~ ! [X10 : $i,X11 : $i,X19 : $i] : ((X3 @ X10 @ X19) | ~(X3 @ X11 @ X19) | ~(X3 @ X10 @ X11)))) | ~ ! [X11 : $i,X19 : $i,X10 : $i] : ((X24 @ X10 @ X19) | ~(X24 @ X10 @ X11) | ~(X24 @ X11 @ X19)) | (X23 @ X5 @ X4) | (X4 = X5) | ~ ! [X11 : $i,X20 : $i,X10 : $i] : (~(X23 @ X10 @ X11) | ~(X23 @ X11 @ X20) | (X23 @ X10 @ X20)) | ~ ! [X9 : $i,X8 : $i] : ((X23 @ X8 @ X9) | ~(X2 @ X8 @ X9))))) = cr) & ((^[X2 : ($i > $i > $o)] : (! [X4 : $i,X5 : $i] : (~(X2 @ X5 @ X4) | ~(X2 @ X4 @ X5)) & ! [X5 : $i,X7 : $i,X4 : $i] : ((X2 @ X4 @ X7) | ~(X2 @ X5 @ X7) | ~(X2 @ X4 @ X5)))) = so) & (asymm = (^[X2 : ($i > $i > $o)] : (! [X4 : $i,X5 : $i] : (~(X2 @ X4 @ X5) | ~(X2 @ X5 @ X4))))) & (trans = (^[X2 : ($i > $i > $o)] : (! [X5 : $i,X7 : $i,X4 : $i] : (~(X2 @ X5 @ X7) | ~(X2 @ X4 @ X5) | (X2 @ X4 @ X7))))) & ((^[X6 : (($i > $i > $o) > $i > $i > $o)] : (! [X2 : ($i > $i > $o)] : (((X6 @ X2)) = ((X6 @ (X6 @ X2)))))) = idem) & ((^[X2 : ($i > $i > $o)] : (! [X7 : $i,X4 : $i,X17 : ($i > $i > $o),X18 : ($i > $i > $o),X5 : $i] : (~ ! [X8 : $i,X9 : $i] : ((X18 @ X8 @ X9) | ~(X2 @ X8 @ X9)) | (X5 = X7) | ~ ! [X9 : $i,X8 : $i] : (~(X2 @ X8 @ X9) | (X17 @ X8 @ X9)) | (X17 @ X5 @ X7) | ~ ! [X19 : $i,X11 : $i,X10 : $i] : ((X18 @ X10 @ X19) | ~(X18 @ X10 @ X11) | ~(X18 @ X11 @ X19)) | ~ ! [X10 : $i,X11 : $i,X20 : $i] : (~(X17 @ X10 @ X11) | (X17 @ X10 @ X20) | ~(X17 @ X11 @ X20)) | ~ ! [X21 : $i] : (~ ! [X3 : ($i > $i > $o)] : ((X3 @ X7 @ X21) | ~ ! [X19 : $i,X10 : $i,X11 : $i] : (~(X3 @ X11 @ X19) | ~(X3 @ X10 @ X11) | (X3 @ X10 @ X19)) | ~ ! [X9 : $i,X8 : $i] : (~(X2 @ X8 @ X9) | (X3 @ X8 @ X9))) | ~ ! [X3 : ($i > $i > $o)] : (~ ! [X20 : $i,X11 : $i,X10 : $i] : (~(X3 @ X10 @ X11) | ~(X3 @ X11 @ X20) | (X3 @ X10 @ X20)) | (X3 @ X5 @ X21) | ~ ! [X9 : $i,X8 : $i] : ((X3 @ X8 @ X9) | ~(X2 @ X8 @ X9)))) | ((X4 != X5) & ~ ! [X3 : ($i > $i > $o)] : (~ ! [X11 : $i,X22 : $i,X10 : $i] : (~(X3 @ X10 @ X11) | ~(X3 @ X11 @ X22) | (X3 @ X10 @ X22)) | ~ ! [X8 : $i,X9 : $i] : (~(X2 @ X8 @ X9) | (X3 @ X8 @ X9)) | (X3 @ X4 @ X5))) | (~ ! [X3 : ($i > $i > $o)] : (~ ! [X9 : $i,X8 : $i] : ((X3 @ X8 @ X9) | ~(X2 @ X8 @ X9)) | (X3 @ X4 @ X7) | ~ ! [X10 : $i,X11 : $i,X19 : $i] : (~(X3 @ X10 @ X11) | (X3 @ X10 @ X19) | ~(X3 @ X11 @ X19))) & (X4 != X7)) | (X18 @ X7 @ X5)))) = confl)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',sev441_1)).
thf(f2,conjecture,(
  ((^[X0 : ($i > $i > $o)] : (! [X3 : $i,X1 : $i,X2 : $i] : (((X0 @ X1 @ X3) & (X0 @ X1 @ X2)) => (join @ X0 @ X3 @ X2)))) = lconfl)),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',locally_confluent)).
thf(f3,negated_conjecture,(
  ~ ((^[X0 : ($i > $i > $o)] : (! [X3 : $i,X1 : $i,X2 : $i] : (((X0 @ X1 @ X3) & (X0 @ X1 @ X2)) => (join @ X0 @ X3 @ X2)))) = lconfl)),
  inference(negated_conjecture,[status(cth)],[f2])).
thf(f4,plain,(
  ((^[X0 : ($i > $i > $o), X1 : $i, X2 : $i] : ((X0 @ X2 @ X1))) = inv) & (irrefl = (^[X3 : ($i > $i > $o)] : (! [X4 : $i] : ~(X3 @ X4 @ X4)))) & (norm = (^[X5 : ($i > $i > $o)] : (! [X6 : $i,X7 : $i] : (~ ! [X8 : $i] : (~ ! [X9 : $i] : ~(X5 @ X8 @ X9) | ~ ! [X10 : ($i > $i > $o)] : ((X10 @ X7 @ X8) | ~ ! [X11 : $i,X12 : $i] : ((X10 @ X11 @ X12) | ~(X5 @ X11 @ X12)) | ~ ! [X13 : $i,X14 : $i,X15 : $i] : (~(X10 @ X13 @ X14) | (X10 @ X15 @ X14) | ~(X10 @ X15 @ X13)))) | ~(X5 @ X7 @ X6))))) & ! [X16 : $i] : ? [X17 : d_unsorted] : (((d2unsorted @ X17)) = X16) & ((^[X18 : ($i > $i > $o), X19 : $i, X20 : $i] : ((X19 = X20) | ! [X21 : ($i > $i > $o)] : (~ ! [X22 : $i,X23 : $i,X24 : $i] : (~(X21 @ X22 @ X23) | (X21 @ X24 @ X23) | ~(X21 @ X24 @ X22)) | ~ ! [X25 : $i,X26 : $i] : (~(X18 @ X26 @ X25) | (X21 @ X26 @ X25)) | (X21 @ X19 @ X20)))) = trc) & ((^[X27 : ($i > $i > $o), X28 : $i, X29 : $i] : (! [X30 : ($i > $i > $o)] : (~ ! [X31 : $i,X32 : $i,X33 : $i] : (~(X30 @ X31 @ X32) | ~(X30 @ X33 @ X31) | (X30 @ X33 @ X32)) | (X30 @ X28 @ X29) | ~ ! [X34 : $i,X35 : $i] : ((X30 @ X35 @ X34) | ~(X27 @ X35 @ X34))))) = tc) & ((^[X36 : ($i > $i > $o), X37 : $i] : (! [X38 : $i] : ~(X36 @ X37 @ X38))) = innf) & ! [X39 : d_unsorted] : (d_unsorted_0 = X39) & ((^[X40 : ($i > $i > $o)] : (! [X41 : $i,X42 : $i,X43 : $i] : (~(X40 @ X41 @ X43) | (X40 @ X41 @ X42) | ~(X40 @ X43 @ X42)) & ! [X44 : $i,X45 : $i] : (~(X40 @ X44 @ X45) | ~(X40 @ X45 @ X44) | (X44 = X45)) & ! [X46 : $i] : (X40 @ X46 @ X46))) = po) & (join = (^[X47 : ($i > $i > $o), X48 : $i, X49 : $i] : (~(! [X50 : $i] : (~ ! [X51 : ($i > $i > $o)] : (~ ! [X52 : $i,X53 : $i] : ((X51 @ X53 @ X52) | ~(X47 @ X53 @ X52)) | ~ ! [X54 : $i,X55 : $i,X56 : $i] : ((X51 @ X56 @ X55) | ~(X51 @ X54 @ X55) | ~(X51 @ X56 @ X54)) | (X51 @ X49 @ X50)) | ~ ! [X57 : ($i > $i > $o)] : (~ ! [X58 : $i,X59 : $i] : (~(X47 @ X58 @ X59) | (X57 @ X58 @ X59)) | ~ ! [X60 : $i,X61 : $i,X62 : $i] : (~(X57 @ X60 @ X62) | (X57 @ X61 @ X62) | ~(X57 @ X61 @ X60)) | (X57 @ X48 @ X50))) & ~ ! [X63 : ($i > $i > $o)] : ((X63 @ X49 @ X48) | ~ ! [X64 : $i,X65 : $i] : (~(X47 @ X65 @ X64) | (X63 @ X65 @ X64)) | ~ ! [X66 : $i,X67 : $i,X68 : $i] : ((X63 @ X68 @ X67) | ~(X63 @ X66 @ X67) | ~(X63 @ X68 @ X66))) & (X48 != X49) & ~ ! [X69 : ($i > $i > $o)] : ((X69 @ X48 @ X49) | ~ ! [X70 : $i,X71 : $i,X72 : $i] : ((X69 @ X71 @ X72) | ~(X69 @ X71 @ X70) | ~(X69 @ X70 @ X72)) | ~ ! [X73 : $i,X74 : $i] : ((X69 @ X73 @ X74) | ~(X47 @ X73 @ X74))))))) & (nfof = (^[X75 : ($i > $i > $o), X76 : $i, X77 : $i] : ((! [X78 : ($i > $i > $o)] : (~ ! [X79 : $i,X80 : $i] : ((X78 @ X79 @ X80) | ~(X75 @ X79 @ X80)) | ~ ! [X81 : $i,X82 : $i,X83 : $i] : ((X78 @ X83 @ X81) | ~(X78 @ X83 @ X82) | ~(X78 @ X82 @ X81)) | (X78 @ X77 @ X76)) | (X76 = X77)) & ! [X84 : $i] : ~(X75 @ X76 @ X84)))) & ((^[X85 : ($i > $i > $o)] : (! [X86 : $i,X87 : $i,X88 : ($i > $i > $o),X89 : $i,X90 : ($i > $i > $o)] : (~ ! [X91 : $i] : (~ ! [X92 : ($i > $i > $o)] : ((X92 @ X89 @ X91) | ~ ! [X93 : $i,X94 : $i] : (~(X85 @ X94 @ X93) | (X92 @ X94 @ X93)) | ~ ! [X95 : $i,X96 : $i,X97 : $i] : (~(X92 @ X95 @ X96) | (X92 @ X95 @ X97) | ~(X92 @ X96 @ X97))) | ~ ! [X98 : ($i > $i > $o)] : ((X98 @ X86 @ X91) | ~ ! [X99 : $i,X100 : $i] : ((X98 @ X100 @ X99) | ~(X85 @ X100 @ X99)) | ~ ! [X101 : $i,X102 : $i,X103 : $i] : (~(X98 @ X103 @ X101) | ~(X98 @ X101 @ X102) | (X98 @ X103 @ X102)))) | (X88 @ X89 @ X86) | (X90 @ X86 @ X89) | ~ ! [X104 : $i,X105 : $i,X106 : $i] : (~(X88 @ X105 @ X106) | ~(X88 @ X104 @ X105) | (X88 @ X104 @ X106)) | ~ ! [X107 : $i,X108 : $i] : (~(X85 @ X107 @ X108) | (X88 @ X107 @ X108)) | (X86 = X89) | ~(X85 @ X87 @ X86) | ~ ! [X109 : $i,X110 : $i] : ((X90 @ X109 @ X110) | ~(X85 @ X109 @ X110)) | ~ ! [X111 : $i,X112 : $i,X113 : $i] : (~(X90 @ X113 @ X111) | (X90 @ X112 @ X111) | ~(X90 @ X112 @ X113)) | ~(X85 @ X87 @ X89)))) = lconfl) & (sconfl = (^[X114 : ($i > $i > $o)] : (! [X115 : $i,X116 : ($i > $i > $o),X117 : $i,X118 : ($i > $i > $o),X119 : $i] : (~ ! [X120 : $i,X121 : $i,X122 : $i] : (~(X118 @ X122 @ X120) | (X118 @ X121 @ X120) | ~(X118 @ X121 @ X122)) | ~ ! [X123 : $i] : (~ ! [X124 : ($i > $i > $o)] : (~ ! [X125 : $i,X126 : $i,X127 : $i] : (~(X124 @ X127 @ X126) | ~(X124 @ X126 @ X125) | (X124 @ X127 @ X125)) | (X124 @ X119 @ X123) | ~ ! [X128 : $i,X129 : $i] : ((X124 @ X129 @ X128) | ~(X114 @ X129 @ X128))) | ~ ! [X130 : ($i > $i > $o)] : (~ ! [X131 : $i,X132 : $i] : ((X130 @ X131 @ X132) | ~(X114 @ X131 @ X132)) | ~ ! [X133 : $i,X134 : $i,X135 : $i] : ((X130 @ X135 @ X133) | ~(X130 @ X134 @ X133) | ~(X130 @ X135 @ X134)) | (X130 @ X117 @ X123))) | ~(X114 @ X115 @ X119) | (~ ! [X136 : ($i > $i > $o)] : (~ ! [X137 : $i,X138 : $i] : ((X136 @ X137 @ X138) | ~(X114 @ X137 @ X138)) | ~ ! [X139 : $i,X140 : $i,X141 : $i] : (~(X136 @ X141 @ X140) | (X136 @ X139 @ X140) | ~(X136 @ X139 @ X141)) | (X136 @ X115 @ X117)) & (X115 != X117)) | (X118 @ X119 @ X117) | ~ ! [X142 : $i,X143 : $i] : (~(X114 @ X143 @ X142) | (X118 @ X143 @ X142)) | (X117 = X119) | ~ ! [X144 : $i,X145 : $i,X146 : $i] : ((X116 @ X144 @ X146) | ~(X116 @ X145 @ X146) | ~(X116 @ X144 @ X145)) | ~ ! [X147 : $i,X148 : $i] : ((X116 @ X148 @ X147) | ~(X114 @ X148 @ X147)) | (X116 @ X117 @ X119))))) & (ind = (^[X149 : ($i > $i > $o)] : (! [X150 : $i,X151 : ($i > $o)] : (~ ! [X152 : $i] : (~ ! [X153 : $i] : (~ ! [X154 : ($i > $i > $o)] : (~ ! [X155 : $i,X156 : $i] : (~(X149 @ X156 @ X155) | (X154 @ X156 @ X155)) | ~ ! [X157 : $i,X158 : $i,X159 : $i] : ((X154 @ X157 @ X159) | ~(X154 @ X157 @ X158) | ~(X154 @ X158 @ X159)) | (X154 @ X152 @ X153)) | (X151 @ X153)) | (X151 @ X152)) | (X151 @ X150))))) & (total = (^[X160 : ($i > $i > $o)] : (! [X161 : $i,X162 : $i] : ((X160 @ X162 @ X161) | (X161 = X162) | (X160 @ X161 @ X162))))) & ((^[X163 : ($i > $i > $o), X164 : $i, X165 : $i] : ((X163 @ X164 @ X165) | (X164 = X165))) = rc) & ! [X166 : d_unsorted,X167 : d_unsorted] : ((((d2unsorted @ X166)) = ((d2unsorted @ X167))) => (X166 = X167)) & ((^[X168 : (($i > $i > $o) > $i > $i > $o)] : (! [X169 : $i,X170 : ($i > $i > $o),X171 : $i] : ((X168 @ X170 @ X169 @ X171) | ~(X170 @ X169 @ X171)))) = infl) & (antisymm = (^[X172 : ($i > $i > $o)] : (! [X173 : $i,X174 : $i] : (~(X172 @ X174 @ X173) | (X173 = X174) | ~(X172 @ X173 @ X174))))) & ((^[X175 : ($i > $i > $o), X176 : $i, X177 : $i] : ((X175 @ X177 @ X176) | (X175 @ X176 @ X177))) = sc) & (term = (^[X178 : ($i > $i > $o)] : (! [X179 : $i,X180 : ($i > $o)] : (~ ! [X181 : $i] : (~(X180 @ X181) | ~ ! [X182 : $i] : (~(X178 @ X181 @ X182) | ~(X180 @ X182))) | ~(X180 @ X179))))) & (mono = (^[X183 : (($i > $i > $o) > $i > $i > $o)] : (! [X184 : $i,X185 : ($i > $i > $o),X186 : $i,X187 : ($i > $i > $o)] : ((X183 @ X185 @ X184 @ X186) | ~(X183 @ X187 @ X184 @ X186) | ~ ! [X188 : $i,X189 : $i] : ((X185 @ X189 @ X188) | ~(X187 @ X189 @ X188)))))) & (refl = (^[X190 : ($i > $i > $o)] : (! [X191 : $i] : (X190 @ X191 @ X191)))) & (symm = (^[X192 : ($i > $i > $o)] : (! [X193 : $i,X194 : $i] : (~(X192 @ X194 @ X193) | (X192 @ X193 @ X194))))) & ((^[X195 : ($i > $i > $o), X196 : ($i > $i > $o)] : (! [X197 : $i,X198 : $i] : (~(X195 @ X198 @ X197) | (X196 @ X198 @ X197)))) = subrel) & ((^[X199 : ($i > $i > $o), X200 : $i, X201 : $i] : (! [X202 : ($i > $i > $o)] : ((X202 @ X201 @ X200) | ~ ! [X203 : $i,X204 : $i] : (~(X199 @ X204 @ X203) | (X202 @ X204 @ X203)) | ~ ! [X205 : $i,X206 : $i,X207 : $i] : (~(X202 @ X207 @ X205) | (X202 @ X207 @ X206) | ~(X202 @ X205 @ X206))) | ! [X208 : ($i > $i > $o)] : (~ ! [X209 : $i,X210 : $i,X211 : $i] : (~(X208 @ X210 @ X211) | (X208 @ X210 @ X209) | ~(X208 @ X211 @ X209)) | ~ ! [X212 : $i,X213 : $i] : (~(X199 @ X212 @ X213) | (X208 @ X212 @ X213)) | (X208 @ X200 @ X201)) | (X200 = X201))) = trsc) & ((^[X214 : ($i > $i > $o)] : (! [X215 : ($i > $i > $o),X216 : ($i > $i > $o),X217 : $i,X218 : $i] : ((X215 @ X217 @ X218) | ~ ! [X219 : $i,X220 : $i] : (~(X214 @ X219 @ X220) | (X215 @ X219 @ X220)) | ((X217 != X218) & ~ ! [X221 : ($i > $i > $o)] : ((X221 @ X217 @ X218) | ~ ! [X222 : $i,X223 : $i,X224 : $i] : ((X221 @ X224 @ X223) | ~(X221 @ X222 @ X223) | ~(X221 @ X224 @ X222)) | ~ ! [X225 : $i,X226 : $i] : (~(X214 @ X226 @ X225) | (X221 @ X226 @ X225))) & ~ ! [X227 : ($i > $i > $o)] : (~ ! [X228 : $i,X229 : $i,X230 : $i] : ((X227 @ X228 @ X230) | ~(X227 @ X229 @ X230) | ~(X227 @ X228 @ X229)) | (X227 @ X218 @ X217) | ~ ! [X231 : $i,X232 : $i] : (~(X214 @ X231 @ X232) | (X227 @ X231 @ X232)))) | ~ ! [X233 : $i] : (~ ! [X234 : ($i > $i > $o)] : ((X234 @ X218 @ X233) | ~ ! [X235 : $i,X236 : $i,X237 : $i] : ((X234 @ X235 @ X236) | ~(X234 @ X237 @ X236) | ~(X234 @ X235 @ X237)) | ~ ! [X238 : $i,X239 : $i] : (~(X214 @ X238 @ X239) | (X234 @ X238 @ X239))) | ~ ! [X240 : ($i > $i > $o)] : ((X240 @ X217 @ X233) | ~ ! [X241 : $i,X242 : $i] : ((X240 @ X242 @ X241) | ~(X214 @ X242 @ X241)) | ~ ! [X243 : $i,X244 : $i,X245 : $i] : ((X240 @ X243 @ X245) | ~(X240 @ X244 @ X245) | ~(X240 @ X243 @ X244)))) | ~ ! [X246 : $i,X247 : $i,X248 : $i] : ((X215 @ X248 @ X247) | ~(X215 @ X248 @ X246) | ~(X215 @ X246 @ X247)) | (X216 @ X218 @ X217) | (X217 = X218) | ~ ! [X249 : $i,X250 : $i,X251 : $i] : (~(X216 @ X251 @ X249) | ~(X216 @ X249 @ X250) | (X216 @ X251 @ X250)) | ~ ! [X252 : $i,X253 : $i] : ((X216 @ X253 @ X252) | ~(X214 @ X253 @ X252))))) = cr) & ((^[X254 : ($i > $i > $o)] : (! [X255 : $i,X256 : $i] : (~(X254 @ X256 @ X255) | ~(X254 @ X255 @ X256)) & ! [X257 : $i,X258 : $i,X259 : $i] : ((X254 @ X259 @ X258) | ~(X254 @ X257 @ X258) | ~(X254 @ X259 @ X257)))) = so) & (asymm = (^[X260 : ($i > $i > $o)] : (! [X261 : $i,X262 : $i] : (~(X260 @ X261 @ X262) | ~(X260 @ X262 @ X261))))) & (trans = (^[X263 : ($i > $i > $o)] : (! [X264 : $i,X265 : $i,X266 : $i] : (~(X263 @ X264 @ X265) | ~(X263 @ X266 @ X264) | (X263 @ X266 @ X265))))) & ((^[X267 : (($i > $i > $o) > $i > $i > $o)] : (! [X268 : ($i > $i > $o)] : (((X267 @ X268)) = ((X267 @ (X267 @ X268)))))) = idem) & ((^[X269 : ($i > $i > $o)] : (! [X270 : $i,X271 : $i,X272 : ($i > $i > $o),X273 : ($i > $i > $o),X274 : $i] : (~ ! [X275 : $i,X276 : $i] : ((X273 @ X275 @ X276) | ~(X269 @ X275 @ X276)) | (X270 = X274) | ~ ! [X277 : $i,X278 : $i] : (~(X269 @ X278 @ X277) | (X272 @ X278 @ X277)) | (X272 @ X274 @ X270) | ~ ! [X279 : $i,X280 : $i,X281 : $i] : ((X273 @ X281 @ X279) | ~(X273 @ X281 @ X280) | ~(X273 @ X280 @ X279)) | ~ ! [X282 : $i,X283 : $i,X284 : $i] : (~(X272 @ X282 @ X283) | (X272 @ X282 @ X284) | ~(X272 @ X283 @ X284)) | ~ ! [X285 : $i] : (~ ! [X286 : ($i > $i > $o)] : ((X286 @ X270 @ X285) | ~ ! [X287 : $i,X288 : $i,X289 : $i] : (~(X286 @ X289 @ X287) | ~(X286 @ X288 @ X289) | (X286 @ X288 @ X287)) | ~ ! [X290 : $i,X291 : $i] : (~(X269 @ X291 @ X290) | (X286 @ X291 @ X290))) | ~ ! [X292 : ($i > $i > $o)] : (~ ! [X293 : $i,X294 : $i,X295 : $i] : (~(X292 @ X295 @ X294) | ~(X292 @ X294 @ X293) | (X292 @ X295 @ X293)) | (X292 @ X274 @ X285) | ~ ! [X296 : $i,X297 : $i] : ((X292 @ X297 @ X296) | ~(X269 @ X297 @ X296)))) | ((X271 != X274) & ~ ! [X298 : ($i > $i > $o)] : (~ ! [X299 : $i,X300 : $i,X301 : $i] : (~(X298 @ X301 @ X299) | ~(X298 @ X299 @ X300) | (X298 @ X301 @ X300)) | ~ ! [X302 : $i,X303 : $i] : (~(X269 @ X302 @ X303) | (X298 @ X302 @ X303)) | (X298 @ X271 @ X274))) | (~ ! [X304 : ($i > $i > $o)] : (~ ! [X305 : $i,X306 : $i] : ((X304 @ X306 @ X305) | ~(X269 @ X306 @ X305)) | (X304 @ X271 @ X270) | ~ ! [X307 : $i,X308 : $i,X309 : $i] : (~(X304 @ X307 @ X308) | (X304 @ X307 @ X309) | ~(X304 @ X308 @ X309))) & (X270 != X271)) | (X273 @ X270 @ X274)))) = confl)),
  inference(rectify,[],[f1])).
thf(f5,plain,(
  (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y1 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & ! [X16 : $i] : ? [X17 : d_unsorted] : (((d2unsorted @ X17)) = X16) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))))) | (Y1 = Y2)))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5))))))))))))))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & ! [X39 : d_unsorted] : (d_unsorted_0 = X39) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1)))))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y5 @ Y4)))))))))) | (Y3 @ Y1 @ Y2))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))))))))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))))))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (Y0 @ Y4 @ Y5))) | (Y5 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y6) | (~ (Y3 @ Y8 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))) | (Y1 @ Y5 @ Y2)) | (Y3 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y5 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))))))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y4 @ Y3 @ Y1) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y8 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y8 @ Y6)))))))))) | (Y3 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y2 @ Y1 @ Y3)) | ((~ (Y5 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y3) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y8 @ Y9))))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y8)) | (~ (Y2 @ Y6 @ Y8))))))))))))))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))))))))))))))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & ! [X166 : d_unsorted,X167 : d_unsorted] : ((((d2unsorted @ X166)) = ((d2unsorted @ X167))) => (X166 = X167)) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3 @ Y1)) | (Y0 @ Y2 @ Y3 @ Y1)))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))) | (~ (Y1 @ Y3))))))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y1 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6))))))) | (~ (Y0 @ Y1 @ Y4 @ Y2))) | (Y0 @ Y3 @ Y4 @ Y2)))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4)))))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1))))))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y7 @ Y6))) | (~ (Y3 @ Y5 @ Y7))))))))))) | (Y2 = Y1)) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y2 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y1 @ Y5)))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (Y5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y2 @ Y1)))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y1)))))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y2 @ Y5 @ Y1) | ((~ (Y5 = Y4)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y1) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y4 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y8 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10))))))))))) | (Y7 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y7 @ Y6)) | (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y7 @ Y8)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y6 @ Y8)))))))))) | (Y3 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6))))))))))))))))))))),
  inference(fool_elimination,[],[f4])).
thf(f6,plain,(
  ~ ((^[X0 : ($i > $i > $o)] : (! [X1 : $i,X2 : $i,X3 : $i] : (((X0 @ X2 @ X1) & (X0 @ X2 @ X3)) => (join @ X0 @ X1 @ X3)))) = lconfl)),
  inference(rectify,[],[f3])).
thf(f7,plain,(
  ~ (lconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (join @ Y0 @ Y3 @ Y1))))))))))),
  inference(fool_elimination,[],[f6])).
thf(f8,plain,(
  (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4)))))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1))))))))))) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y1 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1)))))))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y2 @ Y5 @ Y1) | ((~ (Y5 = Y4)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y1) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y4 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y8 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10))))))))))) | (Y7 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y7 @ Y6)) | (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y7 @ Y8)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y6 @ Y8)))))))))) | (Y3 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))))))))))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))))))))))))))))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y7 @ Y6))) | (~ (Y3 @ Y5 @ Y7))))))))))) | (Y2 = Y1)) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y2 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y1 @ Y5)))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (Y5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y2 @ Y1)))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y1)))))))))))) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y5 @ Y4)))))))))) | (Y3 @ Y1 @ Y2))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))))))))))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3 @ Y1)) | (Y0 @ Y2 @ Y3 @ Y1)))))))))) & (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & ! [X3 : d_unsorted,X4 : d_unsorted] : ((((d2unsorted @ X4)) = ((d2unsorted @ X3))) => (X3 = X4)) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y1 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6))))))) | (~ (Y0 @ Y1 @ Y4 @ Y2))) | (Y0 @ Y3 @ Y4 @ Y2)))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))))) | (Y1 = Y2)))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))) | (~ (Y1 @ Y3))))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y4 @ Y3 @ Y1) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y8 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y8 @ Y6)))))))))) | (Y3 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y2 @ Y1 @ Y3)) | ((~ (Y5 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y3) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y8 @ Y9))))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y8)) | (~ (Y2 @ Y6 @ Y8))))))))))))))))))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (Y0 @ Y4 @ Y5))) | (Y5 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y6) | (~ (Y3 @ Y8 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))) | (Y1 @ Y5 @ Y2)) | (Y3 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y5 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6))))))))))))))))))))))),
  inference(rectify,[],[f5])).
thf(f9,plain,(
  (lconfl != (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (join @ Y0 @ Y3 @ Y1))))))))))),
  inference(flattening,[],[f7])).
thf(f10,plain,(
  (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2)))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y7 @ Y6))) | (~ (Y3 @ Y5 @ Y7))))))))))) | (Y2 = Y1)) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y2 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y1 @ Y5)))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (Y5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y2 @ Y1)))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y1)))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y4 @ Y3 @ Y1) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y8 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y8 @ Y6)))))))))) | (Y3 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y2 @ Y1 @ Y3)) | ((~ (Y5 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y3) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y8 @ Y9))))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y8)) | (~ (Y2 @ Y6 @ Y8))))))))))))))))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4)))))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1))))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3 @ Y1)) | (Y0 @ Y2 @ Y3 @ Y1)))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & ! [X4 : d_unsorted,X3 : d_unsorted] : ((((d2unsorted @ X4)) != ((d2unsorted @ X3))) | (X3 = X4)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y1 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y5 @ Y4)))))))))) | (Y3 @ Y1 @ Y2))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))))))))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))) | (~ (Y1 @ Y3))))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1)))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))))))))))))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))))) | (Y1 = Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (Y0 @ Y4 @ Y5))) | (Y5 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y6) | (~ (Y3 @ Y8 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))) | (Y1 @ Y5 @ Y2)) | (Y3 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y5 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))))))))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & ! [X0 : $i] : ? [X1 : d_unsorted] : (((d2unsorted @ X1)) = X0) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y2 @ Y5 @ Y1) | ((~ (Y5 = Y4)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y1) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y4 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y8 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10))))))))))) | (Y7 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y7 @ Y6)) | (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y7 @ Y8)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y6 @ Y8)))))))))) | (Y3 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y1 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6))))))) | (~ (Y0 @ Y1 @ Y4 @ Y2))) | (Y0 @ Y3 @ Y4 @ Y2)))))))))))) & ! [X2 : d_unsorted] : (d_unsorted_0 = X2) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5))))))))))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
  inference(ennf_transformation,[],[f8])).
thf(f11,plain,(
  (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2)))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y7 @ Y6))) | (~ (Y3 @ Y5 @ Y7))))))))))) | (Y2 = Y1)) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y2 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y1 @ Y5)))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (Y5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y2 @ Y1)))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y1)))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y4 @ Y3 @ Y1) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y8 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y8 @ Y6)))))))))) | (Y3 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y2 @ Y1 @ Y3)) | ((~ (Y5 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y3) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y8 @ Y9))))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y8)) | (~ (Y2 @ Y6 @ Y8))))))))))))))))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4)))))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1))))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3 @ Y1)) | (Y0 @ Y2 @ Y3 @ Y1)))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X0)) != ((d2unsorted @ X1))) | (X0 = X1)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y1 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y5 @ Y4)))))))))) | (Y3 @ Y1 @ Y2))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))))))))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))) | (~ (Y1 @ Y3))))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1)))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))))))))))))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))))) | (Y1 = Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (Y0 @ Y4 @ Y5))) | (Y5 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y6) | (~ (Y3 @ Y8 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))) | (Y1 @ Y5 @ Y2)) | (Y3 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y5 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))))))))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & ! [X2 : $i] : ? [X3 : d_unsorted] : (((d2unsorted @ X3)) = X2) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y2 @ Y5 @ Y1) | ((~ (Y5 = Y4)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y1) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y4 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y8 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10))))))))))) | (Y7 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y7 @ Y6)) | (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y7 @ Y8)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y6 @ Y8)))))))))) | (Y3 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y1 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6))))))) | (~ (Y0 @ Y1 @ Y4 @ Y2))) | (Y0 @ Y3 @ Y4 @ Y2)))))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5))))))))))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
  inference(rectify,[],[f10])).
thf(f12,plain,(
  (total = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y0 @ Y2 @ Y1) | (Y2 = Y1)) | (Y0 @ Y1 @ Y2)))))))) & (cr = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((((((((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y3 @ Y5 @ Y6) | (~ (Y3 @ Y7 @ Y6))) | (~ (Y3 @ Y5 @ Y7))))))))))) | (Y2 = Y1)) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y7 @ Y6)) | (~ (Y4 @ Y5 @ Y7))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y8 @ Y7))) | (Y6 @ Y9 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y2 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7)))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y7 @ Y8))) | (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y1 @ Y5)))))))))) | (((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6)))))))) | (Y5 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y8 @ Y7)) | (~ (Y5 @ Y7 @ Y6))) | (Y5 @ Y8 @ Y6))))))))))))) & (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y6 @ Y8)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y6 @ Y7)))))))))) | (Y5 @ Y2 @ Y1)))))) & (~ (Y2 = Y1)))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5))))))))) | (Y4 @ Y2 @ Y1)))))))))))) & (nfof = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ $i @ (^[Y3 : $i]: (~ (Y0 @ Y1 @ Y3)))) & ((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y2 @ Y1) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y4 @ Y5))) | (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4)))))))))))))))))) & (sconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y4 @ Y3 @ Y1) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y7)))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y4 @ Y8 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y8 @ Y6)))))))))) | (Y3 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y2 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y2 @ Y1 @ Y3)) | ((~ (Y5 = Y3)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y5 @ Y3) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y9 @ Y7)) | (Y6 @ Y9 @ Y8)) | (~ (Y6 @ Y7 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y8 @ Y7)) | (Y6 @ Y8 @ Y7))))))))))))) | (~ (Y0 @ Y5 @ Y1))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((Y7 @ Y3 @ Y6) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y8 @ Y9)) | (~ (Y7 @ Y9 @ Y10))) | (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y9 @ Y8)) | (Y7 @ Y9 @ Y8))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y8 @ Y9))))))))))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y8)) | (~ (Y2 @ Y6 @ Y8))))))))))))))))))))))) & (idem = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((Y0 @ Y1) = (Y0 @ (Y0 @ Y1))))))) & (trsc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (((Y1 = Y2) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (Y0 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y5 @ Y6)) | (~ (Y3 @ Y5 @ Y4)))))))))))))) | (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y5)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1))))))))))) & (symm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) | (~ (Y0 @ Y1 @ Y2))))))))) & (infl = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3 @ Y1)) | (Y0 @ Y2 @ Y3 @ Y1)))))))))) & (so = (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y1 @ Y2)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2 @ Y1)) | (~ (Y0 @ Y1 @ Y2)))))))))) & (irrefl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (~ (Y0 @ Y1 @ Y1)))))) & (subrel = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (Y0 @ Y2 @ Y3))))))))))) & ! [X0 : d_unsorted,X1 : d_unsorted] : ((((d2unsorted @ X0)) != ((d2unsorted @ X1))) | (X0 = X1)) & (norm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (Y4 @ Y5 @ Y6)) | (~ (Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y6 @ Y5)) | (Y4 @ Y6 @ Y5)))))))) | (Y4 @ Y1 @ Y3))))) | (~ (!! @ $i @ (^[Y4 : $i]: (~ (Y0 @ Y3 @ Y4)))))))))))))))) & (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y5 @ Y4)))))))))) | (Y3 @ Y1 @ Y2))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))))))))))))))))) & (term = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y4)) | (~ (Y0 @ Y3 @ Y4)))))) | (~ (Y1 @ Y3))))))))))))) & (po = (^[Y0 : $i > $i > $o]: (((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((Y2 = Y1) | (~ (Y0 @ Y1 @ Y2))) | (~ (Y0 @ Y2 @ Y1)))))))) & (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y2)) | (Y0 @ Y3 @ Y2)) | (~ (Y0 @ Y3 @ Y1)))))))))))) & (ind = (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (!! @ $i @ (^[Y4 : $i]: ((Y1 @ Y4) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((Y5 @ Y3 @ Y4) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (~ (Y5 @ Y8 @ Y7))) | (Y5 @ Y8 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))))))))))))))))))))) & (trc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (Y3 @ Y4 @ Y5)) | (~ (Y3 @ Y6 @ Y5))))))))))))) | (Y1 = Y2)))))))) & (rc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y1 = Y2) | (Y0 @ Y1 @ Y2)))))))) & (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (Y0 @ Y4 @ Y5))) | (Y5 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y6) | (~ (Y3 @ Y8 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))) | (Y1 @ Y5 @ Y2)) | (Y3 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y5 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))))))))))))))) & (antisymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (Y0 @ Y2 @ Y1)) | (Y2 = Y1)) | (~ (Y0 @ Y1 @ Y2))))))))) & ! [X2 : $i] : (((d2unsorted @ (sK0 @ X2))) = X2) & (trans = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) | (~ (Y0 @ Y1 @ Y3))) | (~ (Y0 @ Y3 @ Y2))))))))))) & (inv = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (Y0 @ Y2 @ Y1))))))) & (confl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((Y2 @ Y5 @ Y1) | ((~ (Y5 = Y4)) & (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y9 @ Y8)))))))))) | (Y6 @ Y4 @ Y5)) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (Y0 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8))))))))))))) | ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((Y6 @ Y4 @ Y1) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y8 @ Y7) | (~ (Y0 @ Y8 @ Y7))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y7 @ Y9)))))))))))))) & (~ (Y4 = Y1)))) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9))))))) | (Y7 @ Y1 @ Y6)) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y10) | (~ (Y7 @ Y9 @ Y10))) | (~ (Y7 @ Y8 @ Y9)))))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9)))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y9 @ Y10) | (~ (Y7 @ Y9 @ Y8))) | (~ (Y7 @ Y8 @ Y10))))))))))) | (Y7 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y3 @ Y7 @ Y6)) | (Y3 @ Y8 @ Y6)) | (~ (Y3 @ Y8 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y2 @ Y7 @ Y8)) | (~ (Y2 @ Y6 @ Y7))) | (Y2 @ Y6 @ Y8)))))))))) | (Y3 @ Y1 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y6 @ Y7) | (~ (Y0 @ Y6 @ Y7))))))))) | (Y5 = Y1)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y2 @ Y7 @ Y6)))))))))))))))))))) & (sc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (Y0 @ Y2 @ Y1)))))))) & (asymm = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y1 @ Y2)) | (~ (Y0 @ Y2 @ Y1))))))))) & (mono = (^[Y0 : ($i > $i > $o) > $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y1 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y6))))))) | (~ (Y0 @ Y1 @ Y4 @ Y2))) | (Y0 @ Y3 @ Y4 @ Y2)))))))))))) & ! [X4 : d_unsorted] : (d_unsorted_0 = X4) & (innf = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (~ (Y0 @ Y1 @ Y2)))))))) & (tc = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))) | (Y3 @ Y1 @ Y2)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y4 @ Y6))) | (~ (Y3 @ Y6 @ Y5))))))))))))))))))) & (refl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1)))))),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X3,$thf(sK0 @ X2))],[f11])).
thf(f16,plain,(
  ( ! [X4 : d_unsorted] : ((d_unsorted_0 = X4)) )),
  inference(cnf_transformation,[],[f12])).
thf(f23,plain,(
  ( ! [X2 : $i] : ((((d2unsorted @ (sK0 @ X2))) = X2)) )),
  inference(cnf_transformation,[],[f12])).
thf(f25,plain,(
  (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (Y0 @ Y4 @ Y5))) | (Y5 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y6) | (~ (Y3 @ Y8 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))) | (Y1 @ Y5 @ Y2)) | (Y3 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y5 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6))))))))))))))))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f31,plain,(
  (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y5 @ Y4)))))))))) | (Y3 @ Y1 @ Y2))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))))),
  inference(cnf_transformation,[],[f12])).
thf(f45,plain,(
  (lconfl != (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (join @ Y0 @ Y3 @ Y1))))))))))),
  inference(cnf_transformation,[],[f9])).
thf(f49,definition,(
  spl1_1 <=> (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y5 @ Y4)))))))))) | (Y3 @ Y1 @ Y2))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))))),
  introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition])).
thf(f51,plain,(
  (join = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y5 @ Y4)))))))))) | (Y3 @ Y1 @ Y2))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))))))))))))))))) | ~spl1_1),
  inference(avatar_component_clause,[],[f49])).
thf(f52,plain,(
  spl1_1),
  inference(avatar_split_clause,[],[f31,f49])).
thf(f54,definition,(
  spl1_2 <=> (lconfl = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (join @ Y0 @ Y3 @ Y1))))))))))),
  introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition])).
thf(f56,plain,(
  (lconfl != (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (join @ Y0 @ Y3 @ Y1)))))))))) | spl1_2),
  inference(avatar_component_clause,[],[f54])).
thf(f57,plain,(
  ~spl1_2),
  inference(avatar_split_clause,[],[f45,f54])).
thf(f59,definition,(
  spl1_3 <=> (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (Y0 @ Y4 @ Y5))) | (Y5 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y6) | (~ (Y3 @ Y8 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))) | (Y1 @ Y5 @ Y2)) | (Y3 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y5 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6))))))))))))))))))))))),
  introduced(definition,[new_symbols(definition,[spl1_3])],[avatar_definition])).
thf(f61,plain,(
  (lconfl = (^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (Y0 @ Y4 @ Y5))) | (Y5 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y6) | (~ (Y3 @ Y8 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))) | (Y1 @ Y5 @ Y2)) | (Y3 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y5 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6)))))))))))))))))))))) | ~spl1_3),
  inference(avatar_component_clause,[],[f59])).
thf(f62,plain,(
  spl1_3),
  inference(avatar_split_clause,[],[f25,f59])).
thf(f63,plain,(
  ((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (join @ Y0 @ Y3 @ Y1))))))))) @ sK2)) != ((lconfl @ sK2))) | spl1_2),
  inference(negative_extensionality,[],[f56])).
thf(f65,plain,(
  (((lconfl @ sK2)) = $false) | ((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y2 @ Y3)) => (join @ Y0 @ Y3 @ Y1))))))))) @ sK2)) = $false) | spl1_2),
  inference(xor_proxy_clausification,[],[f63])).
thf(f66,plain,(
  (((lconfl @ sK2)) = $false) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y1 @ Y2)) => (join @ sK2 @ Y2 @ Y0)))))))))) | spl1_2),
  inference(beta-eta_normalization,[],[f65])).
thf(f67,plain,(
  ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK2 @ Y1 @ Y0) & (sK2 @ Y1 @ Y2)) => (join @ sK2 @ Y2 @ Y0))))))) @ sK3))) | (((lconfl @ sK2)) = $false) | spl1_2),
  inference(sigma_proxy_clausification,[],[f66])).
thf(f68,plain,(
  (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ sK3) & (sK2 @ Y0 @ Y1)) => (join @ sK2 @ Y1 @ sK3))))))) = $false) | (((lconfl @ sK2)) = $false) | spl1_2),
  inference(beta-eta_normalization,[],[f67])).
thf(f69,plain,(
  (((lconfl @ sK2)) = $false) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((sK2 @ Y0 @ sK3) & (sK2 @ Y0 @ Y1)) => (join @ sK2 @ Y1 @ sK3))))) @ sK4))) | spl1_2),
  inference(sigma_proxy_clausification,[],[f68])).
thf(f70,plain,(
  (((!! @ $i @ (^[Y0 : $i]: (((sK2 @ sK4 @ sK3) & (sK2 @ sK4 @ Y0)) => (join @ sK2 @ Y0 @ sK3))))) = $false) | (((lconfl @ sK2)) = $false) | spl1_2),
  inference(beta-eta_normalization,[],[f69])).
thf(f71,plain,(
  (((lconfl @ sK2)) = $false) | ((((^[Y0 : $i]: (((sK2 @ sK4 @ sK3) & (sK2 @ sK4 @ Y0)) => (join @ sK2 @ Y0 @ sK3))) @ sK5)) = $false) | spl1_2),
  inference(sigma_proxy_clausification,[],[f70])).
thf(f72,plain,(
  (((lconfl @ sK2)) = $false) | ($false = ((((sK2 @ sK4 @ sK3) & (sK2 @ sK4 @ sK5)) => (join @ sK2 @ sK5 @ sK3)))) | spl1_2),
  inference(beta-eta_normalization,[],[f71])).
thf(f73,plain,(
  (((join @ sK2 @ sK5 @ sK3)) = $false) | (((lconfl @ sK2)) = $false) | spl1_2),
  inference(imp_proxy_clausification,[],[f72])).
thf(f87,definition,(
  spl1_4 <=> (((lconfl @ sK2)) = $false)),
  introduced(definition,[new_symbols(definition,[spl1_4])],[avatar_definition])).
thf(f89,plain,(
  (((lconfl @ sK2)) = $false) | ~spl1_4),
  inference(avatar_component_clause,[],[f87])).
thf(f101,definition,(
  spl1_7 <=> (((join @ sK2 @ sK5 @ sK3)) = $false)),
  introduced(definition,[new_symbols(definition,[spl1_7])],[avatar_definition])).
thf(f103,plain,(
  (((join @ sK2 @ sK5 @ sK3)) = $false) | ~spl1_7),
  inference(avatar_component_clause,[],[f101])).
thf(f104,plain,(
  spl1_4 | spl1_7 | spl1_2),
  inference(avatar_split_clause,[],[f73,f54,f101,f87])).
thf(f114,plain,(
  ( ! [X0 : $i] : ((((d2unsorted @ d_unsorted_0)) = X0)) )),
  inference(superposition,[],[f23,f16])).
thf(f120,plain,(
  ( ! [X1 : ($i > $i > $o)] : (((((^[Y0 : $i > $i > $o]: ((^[Y1 : $i]: ((^[Y2 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (Y0 @ Y5 @ Y4)) | (Y3 @ Y5 @ Y4))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y5 @ Y6))) | (Y3 @ Y5 @ Y4)))))))))) | (Y3 @ Y1 @ Y2))))) & (~ (Y1 = Y2))) & (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (Y0 @ Y4 @ Y5))))))))) | (Y3 @ Y2 @ Y1)))))) & (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y1 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y7)) | (Y4 @ Y6 @ Y5)) | (~ (Y4 @ Y7 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y6 @ Y5) | (~ (Y0 @ Y6 @ Y5)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((Y4 @ Y2 @ Y3) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y5 @ Y7)) | (~ (Y4 @ Y7 @ Y6))) | (Y4 @ Y5 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (Y0 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6))))))))))))))))))))) @ X1)) = ((join @ X1)))) ) | ~spl1_1),
  inference(argument_congruence,[],[f51])).
thf(f121,plain,(
  ( ! [X1 : ($i > $i > $o)] : (((^[Y0 : $i]: ((^[Y1 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y3)) | (~ (Y2 @ Y4 @ Y5))) | (Y2 @ Y4 @ Y3)))))))))) | (Y2 @ Y0 @ Y1))))) & (~ (Y0 = Y1))) & (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y5 @ Y4))) | (Y2 @ Y3 @ Y4))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4))))))))) | (Y2 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y0 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (X1 @ Y5 @ Y4)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))))))))))))))) = ((join @ X1)))) ) | ~spl1_1),
  inference(beta-eta_normalization,[],[f120])).
thf(f134,plain,(
  ( ! [X0 : $i,X1 : $i] : ((X0 = X1)) )),
  inference(superposition,[],[f114,f114])).
thf(f199,plain,(
  ( ! [X2 : $i,X1 : ($i > $i > $o)] : ((((join @ X1 @ X2)) = (((^[Y0 : $i]: ((^[Y1 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (Y2 @ Y4 @ Y3))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y5 @ Y3)) | (~ (Y2 @ Y4 @ Y5))) | (Y2 @ Y4 @ Y3)))))))))) | (Y2 @ Y0 @ Y1))))) & (~ (Y0 = Y1))) & (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y5 @ Y4))) | (Y2 @ Y3 @ Y4))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4))))))))) | (Y2 @ Y1 @ Y0)))))) & (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y0 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y6)) | (Y3 @ Y5 @ Y4)) | (~ (Y3 @ Y6 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5 @ Y4) | (~ (X1 @ Y5 @ Y4)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((Y3 @ Y1 @ Y2) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y4 @ Y6)) | (~ (Y3 @ Y6 @ Y5))) | (Y3 @ Y4 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5))))))))))))))))))) @ X2)))) ) | ~spl1_1),
  inference(argument_congruence,[],[f121])).
thf(f200,plain,(
  ( ! [X2 : $i,X1 : ($i > $i > $o)] : ((((join @ X1 @ X2)) = (^[Y0 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y2)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y3 @ Y2)))))))))) | (Y1 @ X2 @ Y0))))) & (~ (X2 = Y0))) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y4 @ Y3))) | (Y1 @ Y2 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3))))))))) | (Y1 @ Y0 @ X2)))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ X2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y5)) | (Y2 @ Y4 @ Y3)) | (~ (Y2 @ Y5 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y5 @ Y4))) | (Y2 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4))))))))))))))))))) ) | ~spl1_1),
  inference(beta-eta_normalization,[],[f199])).
thf(f201,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : (((((^[Y0 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y2)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y3 @ Y2)))))))))) | (Y1 @ X2 @ Y0))))) & (~ (X2 = Y0))) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y4 @ Y3))) | (Y1 @ Y2 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3))))))))) | (Y1 @ Y0 @ X2)))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ X2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y5)) | (Y2 @ Y4 @ Y3)) | (~ (Y2 @ Y5 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y5 @ Y4))) | (Y2 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4))))))))))))))))) @ X3)) = ((join @ X1 @ X2 @ X3)))) ) | ~spl1_1),
  inference(argument_congruence,[],[f200])).
thf(f203,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((join @ X1 @ X2 @ X3)) = $true) | ((((^[Y0 : $i]: (~ ((((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y3 @ Y2)) | (Y1 @ Y3 @ Y2))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y4 @ Y2)) | (~ (Y1 @ Y3 @ Y4))) | (Y1 @ Y3 @ Y2)))))))))) | (Y1 @ X2 @ Y0))))) & (~ (X2 = Y0))) & (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y4 @ Y3))) | (Y1 @ Y2 @ Y3))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3))))))))) | (Y1 @ Y0 @ X2)))))) & (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ X2 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y5)) | (Y2 @ Y4 @ Y3)) | (~ (Y2 @ Y5 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((Y2 @ Y0 @ Y1) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y3 @ Y5)) | (~ (Y2 @ Y5 @ Y4))) | (Y2 @ Y3 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4))))))))))))))))) @ X3)) = $false)) ) | ~spl1_1),
  inference(iff_proxy_clausification,[],[f201])).
thf(f204,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((join @ X1 @ X2 @ X3)) = $true) | ($false = ((~ ((((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))))) | (Y0 @ X2 @ X3))))) & (~ (X2 = X3))) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (Y0 @ X3 @ X2)))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y3 @ Y4)) | (Y1 @ Y3 @ Y2)) | (~ (Y1 @ Y4 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X3 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y4 @ Y3))) | (Y1 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3))))))))))))))))))) ) | ~spl1_1),
  inference(beta-eta_normalization,[],[f203])).
thf(f205,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : (((((((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))))) | (Y0 @ X2 @ X3))))) & (~ (X2 = X3))) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (Y0 @ X3 @ X2)))))) & (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X2 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y3 @ Y4)) | (Y1 @ Y3 @ Y2)) | (~ (Y1 @ Y4 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2)))))))))))) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((Y1 @ X3 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y2 @ Y4)) | (~ (Y1 @ Y4 @ Y3))) | (Y1 @ Y2 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))))))))))) = $true) | (((join @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_1),
  inference(not_proxy_clausification,[],[f204])).
thf(f207,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((join @ X1 @ X2 @ X3)) = $true) | (((((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))))) | (Y0 @ X2 @ X3))))) & (~ (X2 = X3))) & (~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y1 @ Y3)) | (~ (Y0 @ Y3 @ Y2))) | (Y0 @ Y1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) | (~ (X1 @ Y1 @ Y2))))))))) | (Y0 @ X3 @ X2))))))) = $true)) ) | ~spl1_1),
  inference(and_proxy_clausification,[],[f205])).
thf(f209,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((join @ X1 @ X2 @ X3)) = $true) | ((((~ (!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (Y0 @ Y2 @ Y1))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (Y0 @ Y3 @ Y1)) | (~ (Y0 @ Y2 @ Y3))) | (Y0 @ Y2 @ Y1)))))))))) | (Y0 @ X2 @ X3))))) & (~ (X2 = X3)))) = $true)) ) | ~spl1_1),
  inference(and_proxy_clausification,[],[f207])).
thf(f210,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((join @ X1 @ X2 @ X3)) = $true) | (((~ (X2 = X3))) = $true)) ) | ~spl1_1),
  inference(and_proxy_clausification,[],[f209])).
thf(f237,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((X2 = X3)) = $false) | (((join @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_1),
  inference(not_proxy_clausification,[],[f210])).
thf(f238,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((X2 != X3) | (((join @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_1),
  inference(equality_proxy_clausification,[],[f237])).
thf(f1999,plain,(
  ( ! [X2 : $i,X3 : $i,X1 : ($i > $i > $o)] : ((((join @ X1 @ X2 @ X3)) = $true)) ) | ~spl1_1),
  inference(forward_subsumption_resolution,[],[f238,f134])).
thf(f2002,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((lconfl @ X1)) = (((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (Y0 @ Y4 @ Y5))) | (Y5 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y6) | (~ (Y3 @ Y8 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))) | (Y1 @ Y5 @ Y2)) | (Y3 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y5 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6))))))))))))))))))))) @ X1)))) ) | ~spl1_3),
  inference(argument_congruence,[],[f61])).
thf(f2003,plain,(
  ( ! [X1 : ($i > $i > $o)] : (((((^[Y0 : $i > $i > $o]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((((((((((~ (Y0 @ Y4 @ Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y1 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y8)) | (~ (Y1 @ Y6 @ Y8))))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (Y0 @ Y7 @ Y6)) | (Y1 @ Y7 @ Y6)))))))) | (~ (Y0 @ Y4 @ Y5))) | (Y5 = Y2)) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y3 @ Y7 @ Y6) | (~ (Y0 @ Y7 @ Y6))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y3 @ Y8 @ Y6) | (~ (Y3 @ Y8 @ Y7))) | (~ (Y3 @ Y7 @ Y6))))))))))) | (Y1 @ Y5 @ Y2)) | (Y3 @ Y2 @ Y5)) | (~ (!! @ $i @ (^[Y6 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((Y7 @ Y8 @ Y9) | (~ (Y7 @ Y10 @ Y9))) | (~ (Y7 @ Y8 @ Y10)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((~ (Y0 @ Y8 @ Y9)) | (Y7 @ Y8 @ Y9)))))))) | (Y7 @ Y5 @ Y6))))) | (~ (!! @ ($i > $i > $o) @ (^[Y7 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (!! @ $i @ (^[Y10 : $i]: (((~ (Y7 @ Y9 @ Y8)) | (Y7 @ Y10 @ Y8)) | (~ (Y7 @ Y10 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: ((Y7 @ Y8 @ Y9) | (~ (Y0 @ Y8 @ Y9))))))))) | (Y7 @ Y2 @ Y6))))))))))))))))))))) @ X1)) = $false) | (((lconfl @ X1)) = $true)) ) | ~spl1_3),
  inference(iff_proxy_clausification,[],[f2002])).
thf(f3804,plain,(
  ( ! [X1 : ($i > $i > $o)] : (($false = ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((((((~ (X1 @ Y3 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y0 @ Y6 @ Y5)) | (Y0 @ Y6 @ Y7)) | (~ (Y0 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y6 @ Y5)) | (Y0 @ Y6 @ Y5)))))))) | (~ (X1 @ Y3 @ Y4))) | (Y4 = Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y6 @ Y5) | (~ (X1 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y2 @ Y7 @ Y5) | (~ (Y2 @ Y7 @ Y6))) | (~ (Y2 @ Y6 @ Y5))))))))))) | (Y0 @ Y4 @ Y1)) | (Y2 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y7 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (X1 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y9 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (X1 @ Y7 @ Y8))))))))) | (Y6 @ Y1 @ Y5)))))))))))))))))))))) | (((lconfl @ X1)) = $true)) ) | ~spl1_3),
  inference(beta-eta_normalization,[],[f2003])).
thf(f3805,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((lconfl @ X1)) = $true) | ((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((((((((((~ (X1 @ Y3 @ Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y0 @ Y6 @ Y5)) | (Y0 @ Y6 @ Y7)) | (~ (Y0 @ Y5 @ Y7))))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y6 @ Y5)) | (Y0 @ Y6 @ Y5)))))))) | (~ (X1 @ Y3 @ Y4))) | (Y4 = Y1)) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y2 @ Y6 @ Y5) | (~ (X1 @ Y6 @ Y5))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y2 @ Y7 @ Y5) | (~ (Y2 @ Y7 @ Y6))) | (~ (Y2 @ Y6 @ Y5))))))))))) | (Y0 @ Y4 @ Y1)) | (Y2 @ Y1 @ Y4)) | (~ (!! @ $i @ (^[Y5 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((Y6 @ Y7 @ Y8) | (~ (Y6 @ Y9 @ Y8))) | (~ (Y6 @ Y7 @ Y9)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((~ (X1 @ Y7 @ Y8)) | (Y6 @ Y7 @ Y8)))))))) | (Y6 @ Y4 @ Y5))))) | (~ (!! @ ($i > $i > $o) @ (^[Y6 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (!! @ $i @ (^[Y9 : $i]: (((~ (Y6 @ Y8 @ Y7)) | (Y6 @ Y9 @ Y7)) | (~ (Y6 @ Y9 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: ((Y6 @ Y7 @ Y8) | (~ (X1 @ Y7 @ Y8))))))))) | (Y6 @ Y1 @ Y5))))))))))))))))))) @ (sK278 @ X1))) = $false)) ) | ~spl1_3),
  inference(sigma_proxy_clausification,[],[f3804])).
thf(f3806,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((lconfl @ X1)) = $true) | ($false = ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((((((~ (X1 @ Y2 @ Y0)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (sK278 @ X1 @ Y5 @ Y4)) | (sK278 @ X1 @ Y5 @ Y6)) | (~ (sK278 @ X1 @ Y4 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y5 @ Y4)) | (sK278 @ X1 @ Y5 @ Y4)))))))) | (~ (X1 @ Y2 @ Y3))) | (Y3 = Y0)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5 @ Y4) | (~ (X1 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y1 @ Y6 @ Y4) | (~ (Y1 @ Y6 @ Y5))) | (~ (Y1 @ Y5 @ Y4))))))))))) | (sK278 @ X1 @ Y3 @ Y0)) | (Y1 @ Y0 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y8 @ Y7))) | (~ (Y5 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (X1 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (X1 @ Y6 @ Y7))))))))) | (Y5 @ Y0 @ Y4))))))))))))))))))))) ) | ~spl1_3),
  inference(beta-eta_normalization,[],[f3805])).
thf(f3807,plain,(
  ( ! [X1 : ($i > $i > $o)] : (($false = (((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((((((((((~ (X1 @ Y2 @ Y0)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (sK278 @ X1 @ Y5 @ Y4)) | (sK278 @ X1 @ Y5 @ Y6)) | (~ (sK278 @ X1 @ Y4 @ Y6))))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y5 @ Y4)) | (sK278 @ X1 @ Y5 @ Y4)))))))) | (~ (X1 @ Y2 @ Y3))) | (Y3 = Y0)) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y1 @ Y5 @ Y4) | (~ (X1 @ Y5 @ Y4))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y1 @ Y6 @ Y4) | (~ (Y1 @ Y6 @ Y5))) | (~ (Y1 @ Y5 @ Y4))))))))))) | (sK278 @ X1 @ Y3 @ Y0)) | (Y1 @ Y0 @ Y3)) | (~ (!! @ $i @ (^[Y4 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((Y5 @ Y6 @ Y7) | (~ (Y5 @ Y8 @ Y7))) | (~ (Y5 @ Y6 @ Y8)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((~ (X1 @ Y6 @ Y7)) | (Y5 @ Y6 @ Y7)))))))) | (Y5 @ Y3 @ Y4))))) | (~ (!! @ ($i > $i > $o) @ (^[Y5 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (!! @ $i @ (^[Y8 : $i]: (((~ (Y5 @ Y7 @ Y6)) | (Y5 @ Y8 @ Y6)) | (~ (Y5 @ Y8 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y6 @ Y7) | (~ (X1 @ Y6 @ Y7))))))))) | (Y5 @ Y0 @ Y4))))))))))))))))) @ (sK279 @ X1)))) | (((lconfl @ X1)) = $true)) ) | ~spl1_3),
  inference(sigma_proxy_clausification,[],[f3806])).
thf(f3808,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((lconfl @ X1)) = $true) | (((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((((((~ (X1 @ Y1 @ (sK279 @ X1))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (sK278 @ X1 @ Y4 @ Y3)) | (sK278 @ X1 @ Y4 @ Y5)) | (~ (sK278 @ X1 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (sK278 @ X1 @ Y4 @ Y3)))))))) | (~ (X1 @ Y1 @ Y2))) | (Y2 = (sK279 @ X1))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y0 @ Y5 @ Y3) | (~ (Y0 @ Y5 @ Y4))) | (~ (Y0 @ Y4 @ Y3))))))))))) | (sK278 @ X1 @ Y2 @ (sK279 @ X1))) | (Y0 @ (sK279 @ X1) @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y5 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (X1 @ Y5 @ Y6))))))))) | (Y4 @ (sK279 @ X1) @ Y3))))))))))))))))) = $false)) ) | ~spl1_3),
  inference(beta-eta_normalization,[],[f3807])).
thf(f3809,plain,(
  ( ! [X1 : ($i > $i > $o)] : (((((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((((((((((~ (X1 @ Y1 @ (sK279 @ X1))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (sK278 @ X1 @ Y4 @ Y3)) | (sK278 @ X1 @ Y4 @ Y5)) | (~ (sK278 @ X1 @ Y3 @ Y5))))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y4 @ Y3)) | (sK278 @ X1 @ Y4 @ Y3)))))))) | (~ (X1 @ Y1 @ Y2))) | (Y2 = (sK279 @ X1))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y0 @ Y4 @ Y3) | (~ (X1 @ Y4 @ Y3))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y0 @ Y5 @ Y3) | (~ (Y0 @ Y5 @ Y4))) | (~ (Y0 @ Y4 @ Y3))))))))))) | (sK278 @ X1 @ Y2 @ (sK279 @ X1))) | (Y0 @ (sK279 @ X1) @ Y2)) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((Y4 @ Y5 @ Y6) | (~ (Y4 @ Y7 @ Y6))) | (~ (Y4 @ Y5 @ Y7)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((~ (X1 @ Y5 @ Y6)) | (Y4 @ Y5 @ Y6)))))))) | (Y4 @ Y2 @ Y3))))) | (~ (!! @ ($i > $i > $o) @ (^[Y4 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: (((~ (Y4 @ Y6 @ Y5)) | (Y4 @ Y7 @ Y5)) | (~ (Y4 @ Y7 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: ((Y4 @ Y5 @ Y6) | (~ (X1 @ Y5 @ Y6))))))))) | (Y4 @ (sK279 @ X1) @ Y3))))))))))))))) @ (sK280 @ X1))) = $false) | (((lconfl @ X1)) = $true)) ) | ~spl1_3),
  inference(sigma_proxy_clausification,[],[f3808])).
thf(f3810,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((((((~ (X1 @ Y0 @ (sK279 @ X1))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (sK278 @ X1 @ Y3 @ Y2)) | (sK278 @ X1 @ Y3 @ Y4)) | (~ (sK278 @ X1 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y3 @ Y2)) | (sK278 @ X1 @ Y3 @ Y2)))))))) | (~ (X1 @ Y0 @ Y1))) | (Y1 = (sK279 @ X1))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK280 @ X1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((sK280 @ X1 @ Y4 @ Y2) | (~ (sK280 @ X1 @ Y4 @ Y3))) | (~ (sK280 @ X1 @ Y3 @ Y2))))))))))) | (sK278 @ X1 @ Y1 @ (sK279 @ X1))) | (sK280 @ X1 @ (sK279 @ X1) @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2))))) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (X1 @ Y4 @ Y5))))))))) | (Y3 @ (sK279 @ X1) @ Y2))))))))))))))) = $false) | (((lconfl @ X1)) = $true)) ) | ~spl1_3),
  inference(beta-eta_normalization,[],[f3809])).
thf(f3811,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((lconfl @ X1)) = $true) | ($false = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((((((((~ (X1 @ Y0 @ (sK279 @ X1))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (sK278 @ X1 @ Y3 @ Y2)) | (sK278 @ X1 @ Y3 @ Y4)) | (~ (sK278 @ X1 @ Y2 @ Y4))))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y3 @ Y2)) | (sK278 @ X1 @ Y3 @ Y2)))))))) | (~ (X1 @ Y0 @ Y1))) | (Y1 = (sK279 @ X1))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((sK280 @ X1 @ Y3 @ Y2) | (~ (X1 @ Y3 @ Y2))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((sK280 @ X1 @ Y4 @ Y2) | (~ (sK280 @ X1 @ Y4 @ Y3))) | (~ (sK280 @ X1 @ Y3 @ Y2))))))))))) | (sK278 @ X1 @ Y1 @ (sK279 @ X1))) | (sK280 @ X1 @ (sK279 @ X1) @ Y1)) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((Y3 @ Y4 @ Y5) | (~ (Y3 @ Y6 @ Y5))) | (~ (Y3 @ Y4 @ Y6)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((~ (X1 @ Y4 @ Y5)) | (Y3 @ Y4 @ Y5)))))))) | (Y3 @ Y1 @ Y2))))) | (~ (!! @ ($i > $i > $o) @ (^[Y3 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (!! @ $i @ (^[Y6 : $i]: (((~ (Y3 @ Y5 @ Y4)) | (Y3 @ Y6 @ Y4)) | (~ (Y3 @ Y6 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y4 @ Y5) | (~ (X1 @ Y4 @ Y5))))))))) | (Y3 @ (sK279 @ X1) @ Y2))))))))))))) @ (sK281 @ X1))))) ) | ~spl1_3),
  inference(sigma_proxy_clausification,[],[f3810])).
thf(f3812,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((!! @ $i @ (^[Y0 : $i]: ((((((((((~ (X1 @ (sK281 @ X1) @ (sK279 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (sK278 @ X1 @ Y2 @ Y1)) | (sK278 @ X1 @ Y2 @ Y3)) | (~ (sK278 @ X1 @ Y1 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (sK278 @ X1 @ Y2 @ Y1)))))))) | (~ (X1 @ (sK281 @ X1) @ Y0))) | (Y0 = (sK279 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK280 @ X1 @ Y2 @ Y1) | (~ (X1 @ Y2 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK280 @ X1 @ Y3 @ Y1) | (~ (sK280 @ X1 @ Y3 @ Y2))) | (~ (sK280 @ X1 @ Y2 @ Y1))))))))))) | (sK278 @ X1 @ Y0 @ (sK279 @ X1))) | (sK280 @ X1 @ (sK279 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y4) | (~ (Y2 @ Y5 @ Y4))) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1))))) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y3)) | (Y2 @ Y5 @ Y3)) | (~ (Y2 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4))))))))) | (Y2 @ (sK279 @ X1) @ Y1))))))))))))) = $false) | (((lconfl @ X1)) = $true)) ) | ~spl1_3),
  inference(beta-eta_normalization,[],[f3811])).
thf(f3813,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((lconfl @ X1)) = $true) | ($false = (((^[Y0 : $i]: ((((((((((~ (X1 @ (sK281 @ X1) @ (sK279 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((~ (sK278 @ X1 @ Y2 @ Y1)) | (sK278 @ X1 @ Y2 @ Y3)) | (~ (sK278 @ X1 @ Y1 @ Y3))))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (X1 @ Y2 @ Y1)) | (sK278 @ X1 @ Y2 @ Y1)))))))) | (~ (X1 @ (sK281 @ X1) @ Y0))) | (Y0 = (sK279 @ X1))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((sK280 @ X1 @ Y2 @ Y1) | (~ (X1 @ Y2 @ Y1))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((sK280 @ X1 @ Y3 @ Y1) | (~ (sK280 @ X1 @ Y3 @ Y2))) | (~ (sK280 @ X1 @ Y2 @ Y1))))))))))) | (sK278 @ X1 @ Y0 @ (sK279 @ X1))) | (sK280 @ X1 @ (sK279 @ X1) @ Y0)) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((Y2 @ Y3 @ Y4) | (~ (Y2 @ Y5 @ Y4))) | (~ (Y2 @ Y3 @ Y5)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (X1 @ Y3 @ Y4)) | (Y2 @ Y3 @ Y4)))))))) | (Y2 @ Y0 @ Y1))))) | (~ (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: (((~ (Y2 @ Y4 @ Y3)) | (Y2 @ Y5 @ Y3)) | (~ (Y2 @ Y5 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y3 @ Y4) | (~ (X1 @ Y3 @ Y4))))))))) | (Y2 @ (sK279 @ X1) @ Y1))))))))))) @ (sK282 @ X1))))) ) | ~spl1_3),
  inference(sigma_proxy_clausification,[],[f3812])).
thf(f3814,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((lconfl @ X1)) = $true) | ((((((((((((~ (X1 @ (sK281 @ X1) @ (sK279 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK278 @ X1 @ Y1 @ Y0)) | (sK278 @ X1 @ Y1 @ Y2)) | (~ (sK278 @ X1 @ Y0 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (X1 @ Y1 @ Y0)) | (sK278 @ X1 @ Y1 @ Y0)))))))) | (~ (X1 @ (sK281 @ X1) @ (sK282 @ X1)))) | ((sK282 @ X1) = (sK279 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK280 @ X1 @ Y1 @ Y0) | (~ (X1 @ Y1 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK280 @ X1 @ Y2 @ Y0) | (~ (sK280 @ X1 @ Y2 @ Y1))) | (~ (sK280 @ X1 @ Y1 @ Y0))))))))))) | (sK278 @ X1 @ (sK282 @ X1) @ (sK279 @ X1))) | (sK280 @ X1 @ (sK279 @ X1) @ (sK282 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((Y1 @ Y2 @ Y3) | (~ (Y1 @ Y4 @ Y3))) | (~ (Y1 @ Y2 @ Y4)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (X1 @ Y2 @ Y3)) | (Y1 @ Y2 @ Y3)))))))) | (Y1 @ (sK282 @ X1) @ Y0))))) | (~ (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: (((~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: (((~ (Y1 @ Y3 @ Y2)) | (Y1 @ Y4 @ Y2)) | (~ (Y1 @ Y4 @ Y3)))))))))) | (~ (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y2 @ Y3) | (~ (X1 @ Y2 @ Y3))))))))) | (Y1 @ (sK279 @ X1) @ Y0))))))))))) = $false)) ) | ~spl1_3),
  inference(beta-eta_normalization,[],[f3813])).
thf(f3816,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((((((((((~ (X1 @ (sK281 @ X1) @ (sK279 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK278 @ X1 @ Y1 @ Y0)) | (sK278 @ X1 @ Y1 @ Y2)) | (~ (sK278 @ X1 @ Y0 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (X1 @ Y1 @ Y0)) | (sK278 @ X1 @ Y1 @ Y0)))))))) | (~ (X1 @ (sK281 @ X1) @ (sK282 @ X1)))) | ((sK282 @ X1) = (sK279 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK280 @ X1 @ Y1 @ Y0) | (~ (X1 @ Y1 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK280 @ X1 @ Y2 @ Y0) | (~ (sK280 @ X1 @ Y2 @ Y1))) | (~ (sK280 @ X1 @ Y1 @ Y0))))))))))) | (sK278 @ X1 @ (sK282 @ X1) @ (sK279 @ X1))) | (sK280 @ X1 @ (sK279 @ X1) @ (sK282 @ X1)))) = $false) | (((lconfl @ X1)) = $true)) ) | ~spl1_3),
  inference(or_proxy_clausification,[],[f3814])).
thf(f3818,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((lconfl @ X1)) = $true) | ($false = (((((((((~ (X1 @ (sK281 @ X1) @ (sK279 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK278 @ X1 @ Y1 @ Y0)) | (sK278 @ X1 @ Y1 @ Y2)) | (~ (sK278 @ X1 @ Y0 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (X1 @ Y1 @ Y0)) | (sK278 @ X1 @ Y1 @ Y0)))))))) | (~ (X1 @ (sK281 @ X1) @ (sK282 @ X1)))) | ((sK282 @ X1) = (sK279 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK280 @ X1 @ Y1 @ Y0) | (~ (X1 @ Y1 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK280 @ X1 @ Y2 @ Y0) | (~ (sK280 @ X1 @ Y2 @ Y1))) | (~ (sK280 @ X1 @ Y1 @ Y0))))))))))) | (sK278 @ X1 @ (sK282 @ X1) @ (sK279 @ X1)))))) ) | ~spl1_3),
  inference(or_proxy_clausification,[],[f3816])).
thf(f3820,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((lconfl @ X1)) = $true) | (((((((((~ (X1 @ (sK281 @ X1) @ (sK279 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK278 @ X1 @ Y1 @ Y0)) | (sK278 @ X1 @ Y1 @ Y2)) | (~ (sK278 @ X1 @ Y0 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (X1 @ Y1 @ Y0)) | (sK278 @ X1 @ Y1 @ Y0)))))))) | (~ (X1 @ (sK281 @ X1) @ (sK282 @ X1)))) | ((sK282 @ X1) = (sK279 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK280 @ X1 @ Y1 @ Y0) | (~ (X1 @ Y1 @ Y0))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((sK280 @ X1 @ Y2 @ Y0) | (~ (sK280 @ X1 @ Y2 @ Y1))) | (~ (sK280 @ X1 @ Y1 @ Y0)))))))))))) = $false)) ) | ~spl1_3),
  inference(or_proxy_clausification,[],[f3818])).
thf(f3822,plain,(
  ( ! [X1 : ($i > $i > $o)] : (($false = (((((((~ (X1 @ (sK281 @ X1) @ (sK279 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK278 @ X1 @ Y1 @ Y0)) | (sK278 @ X1 @ Y1 @ Y2)) | (~ (sK278 @ X1 @ Y0 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (X1 @ Y1 @ Y0)) | (sK278 @ X1 @ Y1 @ Y0)))))))) | (~ (X1 @ (sK281 @ X1) @ (sK282 @ X1)))) | ((sK282 @ X1) = (sK279 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((sK280 @ X1 @ Y1 @ Y0) | (~ (X1 @ Y1 @ Y0))))))))))) | (((lconfl @ X1)) = $true)) ) | ~spl1_3),
  inference(or_proxy_clausification,[],[f3820])).
thf(f3824,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((lconfl @ X1)) = $true) | ($false = ((((((~ (X1 @ (sK281 @ X1) @ (sK279 @ X1))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((~ (sK278 @ X1 @ Y1 @ Y0)) | (sK278 @ X1 @ Y1 @ Y2)) | (~ (sK278 @ X1 @ Y0 @ Y2))))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (X1 @ Y1 @ Y0)) | (sK278 @ X1 @ Y1 @ Y0)))))))) | (~ (X1 @ (sK281 @ X1) @ (sK282 @ X1)))) | ((sK282 @ X1) = (sK279 @ X1)))))) ) | ~spl1_3),
  inference(or_proxy_clausification,[],[f3822])).
thf(f3825,plain,(
  ( ! [X1 : ($i > $i > $o)] : (((((sK282 @ X1) = (sK279 @ X1))) = $false) | (((lconfl @ X1)) = $true)) ) | ~spl1_3),
  inference(or_proxy_clausification,[],[f3824])).
thf(f3853,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((sK282 @ X1)) != ((sK279 @ X1))) | (((lconfl @ X1)) = $true)) ) | ~spl1_3),
  inference(equality_proxy_clausification,[],[f3825])).
thf(f4000,plain,(
  ( ! [X1 : ($i > $i > $o)] : ((((lconfl @ X1)) = $true)) ) | ~spl1_3),
  inference(forward_subsumption_resolution,[],[f3853,f134])).
thf(f4001,plain,(
  ($false = $true) | (~spl1_3 | ~spl1_4)),
  inference(backward_demodulation,[],[f89,f4000])).
thf(f4002,plain,(
  $false | (~spl1_3 | ~spl1_4)),
  inference(trivial_inequality_removal,[],[f4001])).
thf(f4003,plain,(
  ~spl1_3 | ~spl1_4),
  inference(avatar_contradiction_clause,[],[f4002])).
thf(f4019,plain,(
  ($false = $true) | (~spl1_1 | ~spl1_7)),
  inference(forward_demodulation,[],[f103,f1999])).
thf(f4020,plain,(
  $false | (~spl1_1 | ~spl1_7)),
  inference(trivial_inequality_removal,[],[f4019])).
thf(f4021,plain,(
  ~spl1_1 | ~spl1_7),
  inference(avatar_contradiction_clause,[],[f4020])).
cnf(s1, plain, spl1_1, inference(sat_conversion,[],[f52])).
cnf(s2, plain, ~spl1_2, inference(sat_conversion,[],[f57])).
cnf(s3, plain, spl1_3, inference(sat_conversion,[],[f62])).
cnf(s6, plain, spl1_2 | spl1_4 | spl1_7, inference(sat_conversion,[],[f104])).
cnf(s17, plain, ~spl1_3 | ~spl1_4, inference(sat_conversion,[],[f4003])).
cnf(s23, plain, ~spl1_1 | ~spl1_7, inference(sat_conversion,[],[f4021])).
cnf(s25, plain, ~spl1_4, inference(rat,[],[s17,s3])).
cnf(s27, plain, spl1_7, inference(rat,[],[s6,s25,s2])).
cnf(s30, plain, ~spl1_1, inference(rat,[],[s23,s27])).
cnf(s35, plain, $false, inference(rat,[],[s1,s30])).
thf(f4022,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s35])).
% SZS output end Proof for theBenchmark